There is this idea of advancing human knowledge and adding to the record of what people know in mathematical research that breaks the analogy down, somewhat. But most people aren't Perelman. They would happily take the million dollar prize. And it is out of the question to do anything other than put your name on the published paper.
But realizing that the primary driver was never actually proving the conjectures, nor understanding the proofs, sheds light into the issue. Many are not satisfied with the prospect of curating and preserving an ever growing collection of discoveries; what they wanted is being the discoverers themselves.
Which to me is mind boggling, because that is not what they have been saying aloud all along. Maybe it's my autism speaking, but I really thought they cared about the resulting knowledge rather than being recognized by their peers. How naïve of me to think that they were above that.
Meanwhile, people who simply enjoy having a tool that facilitates solving problems, because having a solution is their true goal rather than an excuse to obtain recognition or validation, are excited to use this new wonder.
As for the personal swipe: please do better.
https://www.youtube.com/watch?v=ouCVJIpSmEE
(This isn't to say I disagree with you.)
I think what people actually want when they say this is to be the hero. They want the admiration. Which is fine, but at least he honest.
I bet lots of them, who are in it for the love of the game, are truly excited by what is going on.
The noise from AHM and the like can be seen as a drive to intimidate these people into silence.