So why not just use one or more CSPRNGs
That's an extremely good question that has been asked elsewhere with no particular consensus amongst those scientists. There certainly wasn't a fundamental mathematical reason identified saying that you can't. Your hypothesis is correct. If you do:-
A ⊕ B ⊕ C
and only C is good, the construction is still secure even if they are all seeded from the same value as algorithmic ally different RNGs will produce totally different sequences. It is a mathematical feature that combining two poor stream sources produces a disproportionately large decrease in the overall error. And this error drops asymptotically to zero as more sources are combined. Yet this is never done (hypocritically with the exception of A5/1) with no mathematical explanation as to why not.
is it because performance is a concern? There are many applications where it's not
Again an excellent question that has no answer that I can find on this forum$. Excluding some initial short run biases, RC4 isn't that bad. Long run biases are so minuscule that there are currently no practical attacks. And it's very fast. If you add about 6 lines of code to it's output in the form of a Von Neumann extractor, all long run biases disappear. RC4 + VN would then be in the same situation as ISAAC with no known exploits. However there be a consequential speed reduction to only 6% of the original RND. Yet even the resulting ~10 million random bits /s is for some reason considered unacceptable. I too concur there must be an application out there somewhere that needs less than 10 Mb/s of random numbers.
To conclude, the cryptographic community (in as far as this forum goes any way) mysteriously prefers one single RNG that's as fast as humanly possible in all applications and environments from smart buttons to Xeons. So please don't consider this as any form of useful answer. Your good question just raises more questions.
$ My (possibly cinical) explanation is that using AES-CTR serves the interests of the NSA in allowing massive targetting of funding.