It makes an impression like the level was living even when PC wasn't there. I'd say good impression.
I like this idea in general, though I'm not keen on the specifics.
It removes easy healing exploit "go to another level and wait" since monsters would heal too and regain power.
This is kind of an edge case... it's pretty rare that you leave a mostly dead monster on a level. If you really wanted to close this loophole, you could just as easily have it that if the PC has left a level for more than, say, 100 turns, everything on the level is restored to full HP, rather than actually having to calculate monster movement. If the player has been gone much longer, say, 500 turns, you could have it partially populate the level with new monsters as well (though I think you'd have to leave existing monsters, otherwise if you see something nasty, you could just leave the level and wait awhile and it would be gone).
It makes stairs less safe place to store loot. Which discourages a lot from taking more items than you can carry. And it finally makes game less annoying and more challenging.
Not really. Even in 200 turns, if the monsters are just moving randomly, it would be fairly unlikely that they'd stumble into your stash. The flip side of this is that you could potentially exploit this to avoid pursuit. Suppose something is chasing me, but I manage to gain 1 step on it and ascend. Next time I go down, under normal behaviour, it would be right next to me. But under this system, it will wander away randomly and might be a couple steps away. Might not be a big deal most of the time, but it might help killing a vortex or something. Do a lot of players stash items in active levels? Other than doing a big drop before the Air Temple, and maybe leaving a few items at the Darkforge shortcut, I always stash in completely safe areas anyway (Ogre Cave and Barbarian Glade, generally).
It makes farming and ratling traders less annoying because herbs would grow, traders loot would restock, etc.
I really dislike the idea of herbs generating while you're off level. It's an advantage for stable herbs, yeah, but it would be extremely annoying if you have some random herb spawns that you want to come back and deal with later (eg. Big Room).
Leaving compnions/slaves on another level and going for your own business becomes potentially unsafe too unless they're able to handle themselves on their own.
Life with pets is already annoying enough as it is.
Having actual turns passing when you're going up/down stairs would be kind of nasty for speedrunners.