First, despite my vehemence, the original issue was on HD. At this point, I don't even recall how I started about wizards and my attack bonus.I really can’t wrap my head around what the issue even is, here.
The fighter is always better at beating things with sticks, and the wizard is always wasting their time trying to do so, unless they don’t have a melee spell of any kind. (And even then, disengage or dodge might be a better Action)
Even if the wizard has 1 point better attack bonus, so what? The fighter has Action Surge and a Fighting Style, at level 3 they get a significant boost to weapon-based combat efficacy from subclass.
Meanwhile the wizard knows at least half a dozen spells, plus cantrips, and their only proficient finesse weapon deals 1d4 damage.
If they’re a Bladesinger, then being more accurate but doing less damage without burning slots is exactly thematically correct.
If they aren’t, then they’re just a wizard who trained with very few weapons but is pretty damn accurate with those few, and that should be something the player thinks about when determining their backstory.
NUTSHELL: a level 1 fighter and wizard, with equal stats, both have the same attack bonus with weapons. IMO, that makes not sense due to all the training in various weapons and armor a fighter gets prior to starting his adventuring career as where a wizard would train enough to have an idea of what to do with a handful of weapons, but spent the majority of his time mastering his art of magic.
Warriors should hit more often in combat with weapons than non-warriors and there is little support for this, especially at lower levels.