Rankings matter a ton for immediate placement. But many of those top placed students came there with 4 years of experience from Goldman Sachs or something. Still, the trend holds.
Long-term, the individual's ability and work ethic play a larger role than it does in immediate placement. If you continue to study and work every day, you can improve your standing. Finance is meritorious in that way. If you just continue to learn math + stats + coding for years, as if you were part time in a MFE, you can definitely transfer to a higher role as you improve. So choosing a cheaper local position over a better ranked program might not be the best short term decision, but could be the best long term. If that's what it takes to stay in the game. Since high school it has amazed me how many people leave college and stop learning.
I'm a long-distance runner, we have an equivalent mindset. You can only train as hard as you can without blowing up. No injuries allowed. The set back can be years on your fitness with one injury. But you also have to be willing to continue training long enough to improve long-term, even through injuries that have no end. Finance seems similar. There is a high rate on burnout and high turnover. All this depends on how consistently you are able and willing to work, and how long you can continue at that level.
However, if you goal is a top comp top prestige spot or bust, then you better start acting like it. Same thing goes here as it does in running, you can't decide you want to be a world class marathoner if you are 35 and 280. It won't happen. (There are exceptions, sorta, 20something 150 pound world class marathoners with no background come from Ethiopia, Kenya, and recently other eastern African countries all the time. Explaining why would take to much space. But they start at levels that equivalent age Americans can't dream of. It's sorta like the random Ph.D in biology or Psychology you'll hear about being accepted to Princeton or Baruch. They were already smart, and probably with numbers, now they are focused).
TLDR: Short term, yes, choose purely on rank ALL ELSE EQUAL. Otherwise, no, do what you can when you can. Don't brake the bank on a name brand you aren't prepared for.