Yes, you're right, this entire fight is only about which avenues of research are fashionable. For the vast majority of mathematicians, this does not affect th

Yes, you're right, this entire fight is only about which avenues of research are fashionable. For the vast majority of mathematicians, this does not affect their work, and for the mathematicians whose work is directly affected, "answering" this question is like biologists answering the question, "Lions or tigers?" Some people's research will become more fashionable and other people's research will become less fashionable. No answer to this question will be of any more consequence than the philosophical conclusions that a number cannot represent zero quantity, negative quantities are nonsensical, parallel lines never meet, etc. “Woodin showed that if you can just reach the level of the supercompacts, then there’s an overflow and your inner model picks up all the bigger large cardinals as well,” Koellner explained. “That was a sort of landscape shift. It provided this new hope that this approach can work. All you have to do is hit one supercompact and then you’ve got it all.” This is the mathematical equivalent of "640K ought to be enough for anybody." Somebody's going to want something more, or something different, and they're going to do what they want. In the long run, mathematicians only care what assumptions generate neat and/or useful mathematics. In the short run this might affect young researchers' employment prospects and might influence them to choose different problems for that reason.