So, everything is a tradeoff, and nothing is unalloyed good. The tricky part comes in balancing the tradeoffs.
It may be instructive to review the history of open-versus-closed betas with KSP 1.
Once upon a time, when KSP had a major release coming out, there used to be a thing called "Experimentals" where basically anyone who wanted to could sign up for it to get an advance peek at the upcoming release, with the opportunity to submit bugs, feedback, etc. An open beta, basically.
It was that way for a while, and then eventually they shifted to doing a closed beta. Instead of having it open to the general public, they limited it to a relatively small number of people (regular players doing it as volunteers, not paid staff). Once they shifted to that pattern, they stayed that way for the remainder of KSP's lifecycle. The small, closed beta was entirely private, with members not allowed to share what they saw with the public.
So, it's worth asking the question: why would the company do something like that? Obviously, they thought it would be "better" for some reason, but why might that be? (Especially why would they think that's better when they already had the experience of large open betas?)
After all, with the open beta, they'd get far more users providing feedback and trying all sorts of things and finding bugs and so forth, so that must be better, right? Why would they prefer something much smaller?
Well... it turns out that "more" does not necessarily equal "better". Here are a few of the benefits you can get with a closed beta rather than an open one:
Much more actionable feedback:
Pretty much every avid KSP player knows what they like and is ready to share opinions. Lots of them would be happy to report bugs, too. However... reporting in a way that is useful to the developers is a specialized skill, and lots of people don't have that. The only good way to report actionable feedback (either a bug report, or a suggestion) is to file a bug in a bug database. And the bug has to be couched in terms that are actually useful to the devs-- for example, if there's a bug in the program, then the report needs to state a clear and succinct repro case for how to reproduce the bug. Most people don't know how to do this.
If you have a closed beta, you can pick and choose whom to let in, and so you have a population of reasonably-trained people giving you feedback, who can be counted on to be diligent about checking for duplicates before filing, and whose goodwill is assured. As a developer, it's much more useful to have 200 good, actionable bugs than to have 10,000 bug reports & miscellaneous feedback, of which 90%+ are either unactionable or duplicates of each other. Having the huge numbers of bugs not only doesn't help, it actually hurts because now you have to spend your time hunting for the needle in a haystack and triaging endless cruft rather than spending time actually, y'know, developing and fixing bugs.
There are other considerations below, but I think this one's the biggie.
Participants with the right motivation:
What the devs need, from a beta participant, is someone who is motivated to do whatever is necessary to make the game better (even if it's un-fun and boring). What they do not need is someone whose primary motivation is just to have fun, and who wants to get their hands on it earlier rather than later.
Really good beta work is a form of drudgery. "Game tester" may sound like an awesome job title ("Oh man! You mean I get to play games all day and get paid for it? Sign me up!"), but it's actually a lot less fun than it sounds like, even if you're getting paid, which beta participants aren't. Someone who makes a good beta tester needs to be patient and have a high tolerance for repetition and attention to niggling little details. This does not describe most people, and it does not describe the primary motivation of most people who sign up for an open beta.
The devs need people who will do the drudgery, not play the play.
If you only have a reasonably manageable number of people in your beta, and they're all people who have been vetted and approved, then you can have a group chat channel where people can talk back and forth, bounce ideas off each other, exchange thoughts with the devs, etc. This sort of engagement is invaluable. And you can't do that if you've got several thousand random members of the public in your beta. There would be just too many of them, it's not possible to have a coherent chat if there are thousands of people in the channel; plus not all of them would be of good will and on good behavior, so then you'd have to waste more time and resources moderating and so forth. It would be impractical-- the upshot is that with the open beta, it simply wouldn't be practical to have that sort of engagement.
With a closed beta, you can have all the participants sign NDAs so that they can't talk about it with anyone outside the beta. Knowing that they have confidentiality means that the devs can be much more open in talking about what's going on, what their problems are, their concerns about various matters, etc. They can be more free to experiment with ideas that might not pan out and end up needing to be axed or substantially modified. Whereas if it were all out in the open, this is just all sorts of PR disaster just waiting to happen, even if the devs do nothing "wrong". People are funny creatures-- if you show them something they tend to think "yes! that's mine! I'm gonna have that!" and if you then decide not to do it after all, they view this as if you "took it away from them" and can be vocally angry about it in ways that are unhelpful.
With a closed beta, it's easier to manage the message, and the general public doesn't get their hands on it until it's relatively polished.
It's also the case that with confidentiality, this gives the company various PR options, for example they can choose to do a big "ta dah!" unveiling when they actually release. Sometimes that can have value, and it's nice for the company to have the option.
Flexibility & practicality:
With a closed beta, the devs can set things up however is convenient for them (which is what they need), without needing to worry too much about "would this arrangement leave anybody out"-- because they can pick and choose who's in the beta. That can greatly simplify things. For example, back when KSP was still doing Experimentals (open beta), there was one release where they announced that they were going to have this open beta, but only people who had KSP via Steam would be able to participate. There were perfectly good, simple, technical reasons for this: at the time, Steam had good support to meet their technical needs (in terms of releasing builds, having the necessary infrastructure for distribution, etc.) The problem is... the general public viewed this as vile discrimination. Lots of people were super eager to get their hands on the early version... and then became absolutely enraged when they were told that they couldn't. (Especially people who bought the game through the KSP store, because they felt they were being "more loyal and helpful" by doing so.)
Holy mackerel, the KSP forums were a firestorm for a while. It was pretty much a PR nightmare. There was basically no way to tell people "you haven't lost anything and this isn't personal".
Point is: if you have something open to everyone, then the collective community is going to decide that you have to support and allow everyone to do everything, which isn't necessarily what the devs need or want to support when they're busy working their way through the development process. With a closed beta, the devs can simply do whatever is technically easiest and most efficient, and not have to worry about managing the social dynamics of it.
...Anyway. Those are a few of the reasons why a company might choose, for example, a closed beta over an open one. It's worth noting that the folks who made KSP actually tried the open beta for several releases, so they had a pretty good chance to see the advantages and disadvantages of it-- and then, they switched to closed beta and never switched back. I'm not a Squad employee and am therefore not privy to their internal deliberations, but I think those observable facts right there make a pretty strong case that having experienced both options in detail, they decided that on the whole, the closed beta worked better for them than the open one did.
That's all ancient history at this point, of course. You weren't asking about original KSP; you were asking about KSP 2. Well... again, I have no idea what their plans are for KSP 2-- I don't know any more about it than you do. And of course, not every company (or even every game from the same company) is always going to do things the same way all the time; KSP 2 has a somewhat different context than KSP did, so the same factors wouldn't necessarily apply.
But, that said: it totally makes sense to me that they wouldn't do an open beta. They tried an open beta with original KSP for several releases, and eventually gave up on it and never looked back. So, if it worked for KSP, it's at least plausible that it would work for KSP 2 as well.