I don't know, if I were to do a "Hard" Mode with a similar idea to what it seems the OP was looking at...I'd make it far more harsh simply by resurrecting ideas from Older editions of D&D...
HARD/LEGENDARY MODE
- NO DEATH SAVES. Death occurs when PC's hit 0 HP or less. They are DEAD.
- No ASI. What they roll is what they get. No ability score can EVER be higher than 18.
- Characters get 1 HP restored per day without magical healing. 2 HP if they are specifically stating they are resting. This can ONLY change if they are at a "Safe Haven" where they can treat a long rest as 8 hours to restore all hitpoints IF they are not under half their maximum number of HP. If they have less than half their maximum HP, they can restore 1 HD total of HP per day until they are over half their maximum.
These are things taken from older editions already...so, just reverse it a little and I could see the game being harder.
To make it even harder...
- Wizards, Sorcerers and Warlocks stop gaining HD rolls after level 11. They gain 1 HP (NO CON MODIFIER) each level thereafter.
- Fighters, Rangers, Barbarians, and Paladins stop gaining HD rolls after level 9. They gain 3 HP (NO CON Modifier) each level thereafter
- All other classes stop gaining HD rolls after level 10. They gain 2 HP (NO CON MODIFIER) each level thereafter.
- Spells can be disrupted. If the casters are hit, the spell stops working (if they were concentrating) or the spell is not cast if they were in the act of casting I that round but someone acted prior to their action and hit them. The spell is lost.
Something that can make it tougher on spellcasters...but also all around tougher monsters...
-Fighters, Barbarians, Rangers, and Paladins (along with Dwarves who are NOT spellcasters) who are not multi-classed are proficient in ALL saves. Monsters are ALSO proficient in ALL saves.
-Dexterity cannot be used for an ability modifier bonus to hit in melee combat nor be used as a modifier for damage. It can be used to modify the ability to hit with RANGED combat only. Monsters do not suffer this restriction.
You want hard, I think this will be harder for many than what has been listed in some posts on this thread, and yet, this merely replicates a FEW of the rules of Old School AD&D and D&D. It can get even tougher than that (for example, if sticking with BX or BE, we could say that there are no multiple attacks for the most part...or say no multiple attacks until they start getting them around level 15, and that's ONLY for Figthers!!!).