Does anybody know why you max Vault on Quinn first?

Uh....I have no idea where you are getting that info, because no one maxes Vault first. Maybe they did before the rework, but now, Q is too important.

If I had to guess, I'd say that the people maxing Vault first are doing so because it allows them to better burst and kiting certain champions in the laning phase. Since Quinn tends to excel against such champions, she's likely been taken as a counter-pick, which could explain her higher win-rate.

It depends on who you are vs

Someone with range? (Adc, gnar, teemo) LVL Q (can't Attack you with no vision)

someone who is melee? Lvl vault (can't attack you if not in range)

maxing e really isn't that important unless your fighting someone with a hard engage, Her e much to my surprise is counted as an interrupt for most abilities if timed correctly it will cancel lee and akalis dashes, malphite and alistars charges, and interrupt most channeled ults it will however cause you to take damage from a single auto if the enemy has targeted you before you vault them as you are considered in melee range and they have enough time to animate one attack against you before being displaced

well, if you snowball vs a melee it can amplify that, but there´s no real reason to do so unless it´s a very specific matchup.