Does HHH have much say on booking outside NXT?

It strikes me watching NXT that even though I don't necessarily agree with every booking choice they make, in general it almost always makes some amount of rational sense. The progression of storyline and feuds follows a sort of internal logic.

So my question is does HHH have much input at all on how the rest of the company is booked? Not necessarily the TV shows, which I haven't watched in over a decade and the main problem seems to be the writers, but in terms of who goes over on PPV or in feuds. Because as a person that only skims through the monthly PPVs, so much of what they do seems to not make any sense at all.

Why not switch the title onto Strowman when he was the hottest thing going? Why, if you were going to stick with the plan for Roman, blink at the last moment and job him at the exact moment when it will do the most possible damage to the guy? Why end Asuka's streak to Charlotte if you're going to move the belt to Carmella? If you're determined to get the belt onto Carmella, why not have her cash in at Wrestlemania? Why waste Daniel Bryan's first feud in years on freaking Big Cass?

I just have to think, for my own sanity's sake, that whoever is pulling the strings at NXT would have done things differently. Does HHH really have that little sway on Vince? 

​HHH runs the gorilla position, organizing things like timing of matches and kind of running the show, but ultimately Vince is still the guy at the helm of all the stupid decisions they make.  ​