You make one important mistake. You judge the sort of people that police often gets as witnesses (like other criminals, cell-mates etc in whose interest is to cooperate and who get promises from the prosecution), by yourself.
You quite possibly would rather chose longer prison stay/sentence than providing the desired false/ distorted testimony, but many if not most of people might just go along. That is why the practice of rewarding the desired testimony and punishing the refusal of cooperation should be ILLEGAL. Unfortunately at present it is a standard practice and a key tool for the prosecution!