What's exploitative about reskinning a familiar to like a different animal? (within reason, of course.)
It is wanting to eat your cake and have it.
How would you as a wizard player feel about this:
The wizard always is 60ft away. Orcs have the aggressive trait to dash as a bonus action. So you always use prcs and reskin them as goblins, hobgoblins, elves and so on, so you can always reach the wizard in the backrow...
That is what you do. You want to exploit a trait of an animal and because you want to be no boring owl user, you just say your owl is actually a different animal.
That is more or less the same.
I think it was one thing 4e did wrong. Because the outlook of something didn't tell you anything about the abilities and combat something has a player could never know how hard it is to hit an enemy, how many hp something has or what it can do. The only thing which was given for granted was that it should be a fair challenge.
In 5e it is actually the other way around:
If something looks like an orc, you better expect it to dash as a bonus action. If something looks like an owl you better expect flyby attack. If it looks like a falcon you don't.
Edit: or maybe make everything a reskinned dragonborn. So whenever a familiar uses flyby you ready a reskinned dragon breath to kill the familiar and damage everything in its vicinity. What is the drago n breath? A barrage of daggers maybe.
Its just no fair game anymore because it seems arbitrary. If you don't want an owl you won't get abilities of an owl.