The main reason why to use SI units in formula calculations is this:
https://en.wikipedia.org/wiki/Coherence_(units_of_measurement)
I can clearly say from experience that is is very hard to transform formulas to non-SI-unit systems without making mistakes (by far the hardest I meet until now: Fahrenheit ... olala... very dangerous, don't try to land probes on Mars with it ;-) )
For presentation of results you can switch back to your favorite units (I suggest, e.g. using "bar" (the pressure unit) instead of pa (Pascal) often makes sense, or you like "inch" instead of "mm" and the person (not me) you are talking with has ever seen an "inch" and has a feeling what this could be ;-) ). The dimensions of output then should be hand-able (clearly not the case if you say "rail pressure is 100000000 pa" instead of "1000 bar" ... "is o.k." also works ).
Very funny for me (please forgive me) is the plural usage of units I often see (like "meters", "kilograms" etc.) instead of m, kg or Meter and Kilogramm. Or "Watts" instead of W (in memory of James Watt ... or Joan Watson perhaps... ;-) ). Very funny. What's up hehe :-) Is it 1 watt then ? And what to do with 1.2 W ? Plural ? 1.2 watts ? And 0.9 W (less than one) ?
"kg" is furthermore interesting since there is a double meaning of letter "k" in it: The unit is "kg", it has been defined as the basic mass unit of the metric system but it is also 1000 g (1000 Gramm).
What I very often observe is people having problems with electrical units (like charge quantity, energy, power, voltage etc.). and wild mixing these up. So I nearly never see the unit C (Coulomb, or Ampere Second, As) which is the standard unit for electric charge. Even in KSP, which is the most physically based "game" (it's much more than a game) I ever met, I didn't find it yet, but no problem, just something I discovered.
So enough nonsense for today I wish you all a happy Kerbal time !
Tom