I tried that with a Caribbean biotope but ended up putting clownfish into that too - to me a tank without a pair of clownfish is simply wasted space
In general I like the idea but it is kind of tough to execute. If you go for it you may also consider to only add corals and other inverts from the biotope you try to replicate.
But I don't think your idea of stress reduction will actually work.
Even fish that come from the same reef may not encounter all the other fish from that location, simply because they live in different depth levels or regions of the reef (or not even on the reef at all).
For example fish on sandy grounds like gobies will rarely meet with fish from the outer reef like Anthias.
Most fish we keep are quite adaptable to new situations - the ones that are not usually die quickly in captivity.
They also learn to know their tank mates rather quickly. so I don't think the stress issue come from that direction.
When it comes to stress reduction it is more important to consider compatibility of fish and that not all go after the same foods, hiding places,... you name it.
Also in my experience it helps to keep fish in pairs, especially those species that live in bonded pairs in the wild. I think it is more comforting if you are not alone in a strange new environment.
I think the goal has to be to recreate a functioning biotope and not just collect a bunch of colorful fish. There shouldn't be a problem with substituting for example one dottyback, clownfish or angel fish species with another from a different region as long as each has their niche in the tank. That's why I think "collections" of many single angel fish for example will cause more stress than keeping just one pair. Same goes for pretty much all other fish that fill the same niche in a biotope.
