I’ve been thinking of doing a little revision to the way my inevitable 2024 revision of what else goes. (There are two alternative versions of this idea, always in motion, the future is: 5e Killer and _&_.) craphack goes.
I just don’t like the hit dice attached to certain classes in 5e. The grognard in me likes d4 HD wizards. At first I thought I could revise it so there were 3 groups of HD that all made sense together, but unfortunately there are four martials and 5 categories if we use every die, so it’s still a little fucky. Still, here’s the list I came up with:

So, let’s talk a little bit about what Hit Dice are used for in the game. Primarily they are used to determine your Hit Points. You roll your Hit Dice and add your CON Mod to determine how many Hit Points you get per level.
My new proposal is that PCs should add their CON Score (so, 13 instead of +1) at level 1, and then never again. So 1st level PCs would be much more survivable, but their HP total would be lower eventually. I haven’t mathed this out yet, but I really want to try it out.
You also use Hit Dice on a Short Rest to recover lost Hit Points. Perfectly good design, we won’t be altering it here (although we are altering Short Rests–more on that later).
Finally, I want to propose–I don’t know if I like this yet, but I want to propose–using Hit Dice for your Weapon Damage. Perhaps this will be one of the things that sets _&_ apart from 5e Killer. (Are these two products ever going to coalesce? Probably not.) Hit Dice are badly named in the legacy game and new players come with the expectation that their Hit Dice might actually be the dice they use to hit things. Why not indulge in that? Just make every class do the damage of their Hit Dice when they do weapon attacks.
This means you can alter the weapons table substantially, because the differences between weapon damage no longer exist. If we were starting from scratch, we could maybe use the weapons table from Wolves Upon The Coast but we aren’t, we’re starting from the table I’ve had for a couple years and recently redid to include WotC’s Weapon Masteries and then my own Martial Options (forthcoming).
I’m always interested in thoughts about design like this. If you’re interested, feel free to jump on the post, or contact me however you prefer. Stay gold.