How do you implement additional difficulties without pulling stupid shit such as removing the HUD or simply making...

More skillful mechanics. For example, adding a series of moves to a boss with a fair windup that does massive damage/oneshots you if you don't evade/counter most of it, but leaves them open for a long while after so you can beat their ass in return. A good chance of failure with an appropriate amount of reward/payoff when you succeed.

>add more enemies
>reduce enemy reaction times
>add new enemy routines at higher difficulty levels
>further hearing range
>wider sight cones

I dunno. I don't know why "bullet sponge" is the default. I know AI is hard to design, but damn, Halo CE/F.E.A.R. both had incredible enemy AI so it can be done.

I really like how Titanfall 2 did difficulties for Frontier Defense. While there is inflation of stats and enemy numbers, it also gives enemies better equipment. I remember shitting my pants the first time 12 stalkers with EPGs rolled up on my almost dead Northstar, or when the grunts whip out charge rifles on your ass. And removing the radar on max difficulty is one of the few instances of removing hud that I think was implemented well, since it forces communication with your squad if you don't wanna have the harvester assraped by 10 arc ronins.

More enemy waves and greater heals or health but heals at a rate lower than the base difficulty settings making prolonged survival highly dependent on the player’s skill.

What if I gate harder designed levels via difficulties?
So for instance if you choose easy or normal, then the harder stages will be inaccessible and for all you know, non existent.
I wonder if any game has ever done this.

Give the player more things to keep track of, more decisions to make at the same time, tighter margins for making correct decisions, and harsher punishment for making bad decisions.

Well first of all fuck you calling HUD removal “stupid shit”; HUDs and minimaps are both fucking gaaaaaay. I turn them off any time it’s remotely possible.
Secondly I don’t know. It seems like there’s a threshold for realistic difficulty that short of major advancements in enemy AI you can’t really avoid.
Normally what I tend to do is restrict myself to only using certain weapons, or if there’s a skill tree not leveling up things that might be op, etc.

BETTER AI. Unleash those fuckers on harder levels. Make the AI sentient Gods which rain fire down on those who would challenge them. Add new enemies with new quirks, adjust how aggressive they are, change patterns/timings, force the player to use all the tools they have, give them completely new movesets. There is so much you can outside of bullet sponging, but devs are lazy and just want to make movies instead of games.

Change the enemy AI. Make it more aggressive, make it use more moves that would normally be locked in easier difficulties. Less telegraphed attacks. And yeah, make them dish out more damage.
If the game has a cheese strategy, have harder difficulties punish you for trying to use it.

Lots of ways, stupid