I think the only reason those specifically are most well known, is because they capture popular imagination.
Basically, because it’s impossible to see inside black holes to know what’s going on, there’s very few ways to validate ideas. Therefore, outside of a select number of external observational techniques (like radio signals and gravitational waves) to place some limitations, ideas about what happens beyons the event horizon are in the realm of pure math, which people don’t care about unless it either A. Verifiable, or B. Just sounds really cool.
Black Hole hypotheses therefore tend to go one of a few ways:
Scenario 1
Scientist A: Hey if you use this math, black holes can do this thing
Scientist B: That requires this other thing which isn’t true, to be true, and/or breaks this fundamental law
Scientist A: This hypothesis is my precious brain baby and if you talk shit about it I will shatter your knees
Scenario 2
Scientist A: Hey if you use this math, black holes can do this thing
Scientist B: That requires an assumption we can’t, or have yet to, verify is true (almost always somehow related to string theory)
Scientist A: This hypothesis is my precious brain baby and if you talk shit about it I will shatter your knees
Scenario 3:
Scientist A: Hey if you use this math, black holes can do this thing
Scientist B: Okay the math checks out as one of X number of possibilities with that same math, but there’s know way to tell which, if any of these would be true (equations with multiple valid solutions, almost always related to spacetime topology)
Scientist A: Heehee numbers do funni
ETA: The specific subcategories of hypotheses you mentioned also have an inherent advantage of not having to deal with singularities. Why that’s good: Einstein’s theories say infinite density impossible. With singularity, can’t connect quantum theory to relativity theory. No quantum gravity make math bb’s big sad. Solution? Instead of squoosh matter really tiny, just send it somewhere else! They aren’t the only frameworks that avoid singularities, but definitely the coolest sounding and least complicated