While I'm not going to disagree with what your going with, I think your stopping far too short of what it could be. Why stop at simply creatures (or just tames) taking naps? Why not have them react to your presence, (with more than just a head turn), and how about you being able to interact with them after the tame, and not just having them be nothing more than living, breathing weapons and transportation, which does nothing more than stand in a singe spot with nothing to do at all times your not upon them. Wouldn't it be nice to say, be able to play a game of fetch with your dire wolves/raptors/(InsertFavoriteTameHere)? Toss out a stick or bone and watch them eagerly dash to retrieve it and bring it back to you, then have them prance before you in delight and anticipation as you pick it up to throw again.
Or what if they were simply capable of expressing delight or concern toward you? Say you were to take your rex/allo/(OtherLargeDino) out to go level or something, leaving behind in your walled base, your wolves, raptors, sabers etc.etc. Now say your away for several in-game days, doing whatever it is you went to do before you and your tame of choice step back into the walls of your compound. What if as you slide down from your mount, all your other tames that were milling about anxiously, rushed towards you in glee. The sabers rubbing against your legs, raptors nuzzling against you shoulder, while the wolves try jumping on you, nearly knocking you over before they start running in circles around you in excitement; all because you came back to them safe and sound. Or what if even....

If you have any imagination,(mine's OVERACTIVE, if you couldn't tell.), then I think you can just begin to see how much depth a mod that would make tames act 'immersively' would be, and while I am not mod developer, I can only speculate that the amount of time that would be need to create a mod of that complexity and depth, would be tremendous; especially if done properly. And having been here from near the begin of this mod, having seen how much effort Burgesssssss has invested in it, I'm certain that he's one that would do it properly.

However, given how infrequently that Burgesssssss has been active on here lately, I get the feeling that either time is a precious commodity for him, with little to spare for such an endeavor, or the motivation for working on Ark mods has waned. (Or it could I suppose, be due to the.... simplicity, of the majority of comments these days.) So the likely hood of him taking up your challenge is... slim. (But hey, I'd love to be proven wrong if my interpretation is mistaken.)

However I didn't post just to rain on your parade, have you by chance heard of this mod?

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=1785800853

I've not used it myself yet, but have followed it for a short time, they seem to be attempting exactly what you are seeking.

I too was going to suggest Transcendence...

@Burgesssssss
hehe.. I would say great minds think alike, but I'm just a user of your mod....

Well, mainly... My thing is, I WAS going to include a LOT originally, but I don't want to pressure the dude to do that many things without pay. Lmao

At any rate, yeeaahhh I guess I could use Transcendence, never heard of it. Hope it works with the latest DLC, if it doesn't I'll just die I guess.

Good work on Immersive Taming, I hope ya make more stuff like this in the future! :)) I love your mods.