This all began with me discussing my character, an elf wizard. Regardless, dagger, staff, or any weapon wizards are proficient with, take your pick. A wizard SHOULD NOT have the ability to hit as often in melee or ranged combat as a FIGHTER, even at level 1. Period.Wizard isn't proficient in short sword, so no proficency bonus. Advantage, fighter.
If you're a bladesinger, then the training argument is out the window as bladesingers get their 1 weapon proficiency as part if extensive martial training in it.
Your example high elf wizard vs lizardman ranger actually only exceeds the martial character with a dagger, the bow selected for elven training, or light c-bow -- it falls behind on all other weapons, including other finesse or ranged weapons. Your argument is very narrow but you're trying to limit the discussion to your narrow point to hide the deficiencies. This is called special pleading. And that's only looking at attack bonuses. Expand to a broader look at combat and it's worse.
No one is going to convince me otherwise. The universal proficiency bonus applying equally to all things is at fault and should be reversed to prior editions. I'm done and not watching this further. Have fun with it and I'll work on my house-rules, like I've had to do with much of 5E...