Despite the popular adage, human ingenuity is limited. We can distribute more hard puzzles than puzzle solver can solve.
All else equal, if more puzzles exist than we can solve, we should solve puzzles that help advance our goals.
If we can show more important problems exist, it could be possible to make a good faith attempt at trying to see from the point of view of someone who thinks some puzzles should be ordered after other puzzles.
In that frame, the mere existence of all puzzles might be enough to justify many problems (even some "suboptimal" problems lower down the list), but there would also exist problems so uninteresting that their mere existence is not enough.
(All that being said, I'm not entirely sure why I bothered typing all of that in response to a rethorical question... but I suppose you could see arguing as a puzzle, and isn't the existence of that puzzle enough? :P)
The way to think about mathematics is that it’s charting what’s possible and developing new techniques to explore the various frontiers of mathematics. Figuring out practical applications happens later, once you’ve explored. Both are useful but you don’t get the latter without the former. Additionally the skill sets may differ because some people are driven by researching novelty while others are motivated by figuring out novel applications.
There’s so many stories of mathematicians thinking they were working on something useless only for it to become critically valuable. I vaguely recall a story from college about a discrete mathematician that intentionally worked on a “useless” problem space only for that to become the basic research of some branch of digital cryptography decades later.