Infernape Line, Pinsir, and New Illustration Rares Revealed from “Crimson Haze!”

[Yaginku]

It's not necessarily closed design space because you can still design that same pokemon, just of a different type.

I don't think you understand the concept. If you've prevented the creation of something through a previous design, even if it's just a single type, that is a closed design space. It's really not that deep.
Also, Rain Dance does not close any design spaces, it just overrides one of the core rules of the game for a relatively low price of getting a Stage 2 online. You can get a Stage 2 online on Turn 2 with Rare Candy (which also ruins the design space for Stage 1s, but that's another discussion).

ADP may have been a mistake but it did not limit design space in anyway. It might invalidate single prizers but that didn't mean they couldn't design certain single prizers at all.

I really don't understand your logic, because in one sentence you say something isn't an example of something, and then in the next one you present an exact definition of how that something is that thing. Literally the concept of "limiting a design space" is defined as putting strong restrictions on what elements you can design in that space. If a card needs to meet certain standards to be viable, that is literally a limited design space. If it's because of another, single card, that card is limiting that design space.

However, history has shown that this mechanic isn't problematic and unhealthy as you think it is.

History has shown that this mechanic, despite existing alongside some ridiculously broken cards, still manages to be playable. We are talking about Baxcalibur, a card that is a part of a playable deck when things like Charizard ex or Genesect V exists.