People typically aren't stuck on minimum wage because the powers that be won't let them have a decent wage. Most adults are not on minimum wage ( in the US, less than 2% as of 2022; in the UK, low pay accounts for less than 4% as of 2024 ).

There's something to be said for the rich taking advantage of folks, but ... bothering worrying about abstract rich guy metrics like making the GDP go up is not going to help anyone get out of their situation.

Sure, focus on other aspects of politics like making education affordable, strengthening unions, etc things that will help you achieve your goals or help you once you've achieved your goals. However, there's a lot one can directly do to address their situation that's a lot less abstract than "vote for a representative, to write a bill, to potentially help you, to possibly get passed by your legislature, and possibly get passed by your executive branch (or your equivalent process)."

... and even then that latter concept has little to do with "why someone on minimum wage should pay attention to the GDP."