I think there is an interesting underlaying assumption to OP's perspective.
If science is currently used by people when useful and ignored when not useful, that is essentially a criticism of the corruption of people (intellectual dishonesty), but also presumes that science is some kind of force that is inherently intellectually honest, or that it should hold some form of authority.
I think it's a strange assumption to place authority into a system of unraveling mysteries of nature. Science isn't an organisation. It can't be held accountable. It's a giant umbrella, with both corrupt and pure forces working underneath that umbrella. Some science is done to hide secrets (think corporation funded studies to prove safety of tabacco), some science is done purely to make money (think inventing new medicine that replaces existing medicine not by being better, but by being different so the patent length is renewed). There are nearly infinite pure and infinite corrupted reasons for doing science and being done by people most likely smarter than you and me. The publish or perish needs have led to a reproduction crisis in a lot of different scientific fields.
Should "science" hold more authority? If so, which people or organisations would wield that autority in the name of science?
The essential field of conflict is often the idea of "scientific consensus". This is a way how science can be wielded as as stronger sword in politics. After all, if all or most scientists agree, it's probably true, right? Of course this politicizes the science field and puts stronger political motives in making sure which scientists succeed and which do not, regardless of truth content. Unless, I guess, you would claim that politics is in the business of persuing truth, in which case we'll have this talk again after you've followed politics a little longer.
Of course there is merit to this idea of scientific consensus as much like the god of the gaps with evolution, one can forever play a game about the things you don't know or prevent politics on acting on scientific studies by claiming that we don't have sufficient data yet (protip: we never have sufficient data). So to put an end to that game and also to cover politicians asses the idea of scientific consensus helps alleviate some of those tensions.
But then I'm reminded of Einstein. There was the book "Hundred authors against Einstein" (which was in the end 47 authors of which 4 scientists) to which he responded: "Why 100? If I were wrong, one would have been enough."