A recent post on reddit (ok not that recent at a year ago) discussed the idea of gaining an exhaustion level whenever you're knocked unconcious. This definitely adds an extra layer of challenge to the game where you can't let a character drop too many times without there being some harsh consequences. And the rules of exhaustion are pretty harsh. For those without handy access to The Player's Handbook I'll copy in the section from the SRD for the rules of exhaustion at the bottom of this post.
Keep in mind that exhaustion can only be removed with time or the 5th level spell Greater Restoration. This limits the design space of the rule quite a bit. Too many features that grant exhaustion (such as the Frenzy ability of the Path of the Berserker) would kill a player or make the feature unusable.
But, you might have a feat like this:
Exceed the Limits
Increase your Wisdom, Intelligence or Charisma score by 1.
You may gain a level one spell slot as a minor action. Whenever you do so, suffer one level of exhaustion.
So, perhaps it isn't completely limited. I could certainly see designing some especially potent spells, feats or features that tied off of exhaustion as a balancing point. Still, it's a thin line to walk.
Exhaustion
Some special abilities and environmental hazards, such as starvation and the long-term effects of freezing or scorching temperatures, can lead to a special condition called exhaustion. Exhaustion is measured in six levels. An effect can give a creature one or more levels of exhaustion, as specified in the effect’s description.
| Level | Effect |
|---|---|
| 1 | Disadvantage on ability checks |
| 2 | Speed halved |
| 3 | Disadvantage on attack rolls and saving throws |
| 4 | Hit point maximum halved |
| 5 | Speed reduced to 0 |
| 6 | Death |
If an already exhausted creature suffers another effect that causes exhaustion, its current level of exhaustion increases by the amount specified in the effect’s description.
A creature suffers the effect of its current level of exhaustion as well as all lower levels. For example, a creature suffering level 2 exhaustion has its speed halved and has disadvantage on ability checks.
An effect that removes exhaustion reduces its level as specified in the effect’s description, with all exhaustion effects ending if a creature’s exhaustion level is reduced below 1.
Finishing a long rest reduces a creature’s exhaustion level by 1, provided that the creature has also ingested some food and drink.