Rules option for DnD 5E, specifically for legendary and mythical monsters that tend to be the ones with the most HP:
'Attacks from legendary or mythical monsters hit automatically if they require an attack roll and the effects of the attack would not give the target a condition.
Legendary resistances of monsters can only be used against effects that can be assigned to the spell schools abjuration, illusion, transformation or enchantment. Otherwise, monsters can still use their Legendary Resistance to pass saving throws against any effect that would give the monster one or more conditions. In case of doubt, the DM decides.
After a monster has used Legendary Resistance, its movement rate is halved until the end of its next turn. The damage caused by the monster's attacks that require attack rolls is also halved until the end of the monster's next turn after using Legendary Resistance.
(These rules can ensure that battles are both shorter and more exciting due to the higher damage dealt by both sides.
The battles also become more dangerous, making PCs think twice about taking the risk. Creativity is encouraged when considering alternative strategies for conflict resolution. Both ensure that there will be fewer battles overall, which remain the most time-consuming scenes in the game.
The increased risk also makes combat itself more creative when searching for ways to damage the enemy or use the environment for a tactical advantage. It also encourages the player characters to improve their supply of healing options, e.g. through the help of NPCs that can cast healing spells.)'
Rules option for DnD 5E, specifically for legendary and mythical monsters that tend to be the ones with the most HP:
'Attacks from legendary or mythical monsters hit automatically if they require an attack roll and the effects of the attack would not give the target a condition. Legendary resistances of monsters can only be used against effects that can be assigned to the spell schools abjuration, illusion, transformation or enchantment. Otherwise, monsters can still use their Legendary Resistance to pass saving throws against any effect that would give the monster one or more conditions. In case of doubt, the DM decides. After a monster has used Legendary Resistance, its movement rate is halved until the end of its next turn. The damage caused by the monster's attacks that require attack rolls is also halved until the end of the monster's next turn after using Legendary Resistance.
(These rules can ensure that battles are both shorter and more exciting due to the higher damage dealt by both sides. The battles also become more dangerous, making PCs think twice about taking the risk. Creativity is encouraged when considering alternative strategies for conflict resolution. Both ensure that there will be fewer battles overall, which remain the most time-consuming scenes in the game. The increased risk also makes combat itself more creative when searching for ways to damage the enemy or use the environment for a tactical advantage. It also encourages the player characters to improve their supply of healing options, e.g. through the help of NPCs that can cast healing spells.)'
Scribbled together based on this post and its comments as well as some additional ideas I've had.
EDIT: Fixed something that got lost in automatic translation.