House rule for overnight healing: opinions wanted

Joddy37 said:

. Until now, after nearly 8 sessions, I can say that full healing after a long rest seems to detach the characters from the environment, the adventure, and generally from the world, a bit. Every day seems to feel like a fresh start, and characters feel like nothing deadly or dangerous happened the day before.

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This is what I am worried about.

We use Zarusthustran's suggestion for accounting for lingering wounds through exhaustion effects. Our houserule looks like this:

WOUND LEVELS

This optional rule allows for lingering wounds in Dungeons & Dragons while keeping hit point recovery as is. To keep things abstract and simple, you’d take 1 level of exhaustion (PHB 291) when you suffer a critical hit (this would be in place of increased damage) or drop to 0 hp.

To offset the negative modifiers associated with wound levels, restoration spells have been improved to allow them to remove more exhaustion effects. Lesser restoration now removes one level of exhaustion and greater restoration removes all levels of exhaustion.