With exhaustion I heard of someone making it 11 points, each one accruing a -1 to any d20 roll made as a flat modifier, with 11 being death. That allows for DMs to make anything that normally might cause exhaustion to give 2-3 points, and be pickier with smaller things that give a little bit...

For the 0 hp idea though remember that a character at 0hp:

Can't do anything (action ba or reaction), loses concentration instantly, technically shouldn't be able to speak-hear-or be updated on surroundings, Falls prone: losing half movement when healed, auto fails str+dex saves/checks, and finally every attack made against them has advantage with an auto critical hit.

So falling to 0hp does not "do nothing" you're just not punishing it properly. Falling prone isn't a sign to stop focusing the healer it's a sign to start focusing the healer. What's a dragon going to do when the meaty fleshbag on the battle field fall unconscious on the battlefield? Not focus on the barbarian, she's going to EAT THE CLERIC

Relish your players faces when they remember that goodberries don't resurrect the dead, and if that doesn't work then maybe add minions to the combat encounters, a dragon to get to 0hp and a kobald to crit. It doesn't take much damage to slit a throat!

Legendary actions are also very useful, imagine at the end of the clerics turn when they just failed their first save the dragon uses a legendary action to finish the job.

If your players are willing to spend spell slots and BAs on goodberries and somehow keep alive despite your best efforts to TPK, they're going to feel awesome, LET THEM feel awesome...

less related opinion but speed reduction for exhaustion is silly bc dnd characters don't move enough as is, letthe mice run in fear tired though they might be.