Arriving at the Jool system, why Tylo for capture?

[magnemoe]

Yes Tylo has benefits but would not Laythe work just as well? Yes Tylo leaves with Pe at Tylo who is nice then going for the outer moons. But for Laythe or Vall Laythe should work better? 
And how about Jool itself? 
Yes it would require using Tylo or Laythe to lift Pe afterward but Oberth effect close to Jool should be huge. 

[The Aziz]

Gravity assist at Tylo will steal a bit from the energy you have, Jool won't do it on its own, it's a normal flyby in that case.

Sure, other moons would slow you down but not at the same level as Tylo, which is the largest moon there. It's not only Kerbin-sized, but you also can nearly skim the surface for better effect.

You can always get a free capture through Tylo, then lower the Pe so that is crosses Laythe or Vall, whatever you're aiming for, and wait for it to come around. While keeping an eye on Tylo crossing your trajectory every now and then.