Indeed. My research (in statistics) is primarily methodological: I invent and describe methods that might be useful, and on a good day prove some theoretical results demonstrating that they might be useful. There's nothing to replicate there.
Citations can be a useful metric here, particularly if you can identify citations of people actually using the method (as opposed to people just mentioning it in passing, or other methodological researchers comparing their own methods to it).
Well, I'm talking about a math paper. So to me, it's the same as a code review. Someone has to go over the logic and proofs, and double check no mistakes are made.
The number of people who did and gave their approval would be a good indicator I can trust the paper.
What does a citation do that's better then this?
For experiments, or non math papers, you might need something more robust. I think mostly because reviewing the paper isn't really reviewing the full study, but only what the researcher put in the paper. So it is very hard to review methodology and details to be sure they followed proper protocols, etc. You'd need someone to have been reviewing the study as it is happening, and not just the output paper from it.
A citation indicates that other people actually care about the content of the paper.
Consider Researcher A, who has one paper with a hundred citations, and Researcher B, who has ten papers with two citations each. Probably Researcher A has made a larger contribution.
Whether you're in math or any other field, the fact that a paper is correct or reasonable enough to make it past peer review doesn't mean anybody gives a shit about it.
Citations can be a useful metric here, particularly if you can identify citations of people actually using the method (as opposed to people just mentioning it in passing, or other methodological researchers comparing their own methods to it).