Aside from common sense ruling on sound (I mean, have you ever heard a spider?), the advantages I cited are all pretty direct applications of game terms and statistics. The rules on hiding in the PHB stipulate that, in order to hide, a character needs to be totally obscured. A Tiny creature is going to be totally obscured by much smaller objects than even a Small creature. Spiderclimb, the ability for the spider to climb up almost any surface, and into crevices in the ceiling, for instance, is right there in the statblock. There's more to "RAW" than skill modifiers.
By RAW, a spider is able to hide in tons of situations where a humanoid won't even be allowed a roll. (Total concealment.) By RAW, a spider is able to climb into hiding spaces a humanoid could never reach. (Spiderclimb.) The balance issues are handled by common sense and broader thinking on the part of the DM.
If, as a Druid, I wildshaped into a spider to sneak into a treasure vault, and the DM called for a stealth check while I was climbing along the ceiling of a corridor, and, upon a low roll, told me that the goblins playing dice in the room around the corner, noticed me, I would be beyond cheesed.
By the RAW a lion is stealth +6 and a cat is stealth+4 both as "stealthy" and frankly i have not heard ever in my life a human intelligence cat or a human intelligence lion sneaking up on me either... but i a pretty sure that in a DND 5e game dealing with lots of fantastic creatures your players and perhaps others would be at least inclined to bat an eye if they got jumped in darkness by an approaching druid-lion without any check of their character's perception chances.
Now, i am not, again as stated earlier, saying you are wrong for any ruling you want to put into your games. You can rule spiders or cats or lions all unnoticeable in all sorts of situations all day and all night long... I have not one problem with that at all.
have a blast.
Knock yourself out.
But...
Just sayin'...
again...
the more beautifully creative additional abilities you choose to add to "creatures" (or really any game element) that can also be accessed by player abilities - well the more you hit any planned balance upside the head with the Great Club of IRL and after a while with enough hits balance may be needing to start making death saves.
heck, if i knew a GM was into this kind of animal empowerment, i would be looking up venom potencies IRL for my next druid.
So have a ball and go for it.