The wizard's current d6 is still too low for level one and two.
All classes should get a bonus to HP at level 1. Determined by the setting's grittiness level.
Gameplay wise, the wizard's and fighter's HP are too close at higher levels considering their combat role options and specialties.
A wizard starting with 5 bonus HP but having a d4 HD gives them a better HP cushion for Tier 2 but keeps their HP within striking range past high tier 2 and beyond.
But again, is that because the Wizard's hit points are too high relative to the incoming damage, or that the fighter's are too low relative to that same incoming damage?
Around me, wizards still get smacked down when they make themselves obvious to the enemy. Fireballs suck, so intelligent enemies will focus fire on targets that can launch them when they can. So, wizard hit points don't seem to high, to me.
Again, why not raise fighter hit points to cover that balance issue?