Eh it's not about perjury, it's about due process and assymetry of power. The police have the means to record everything at little cost and with no reasonable excuse to not do it. The absence of recordings is a reasonable indicator that the cops are hiding things.

We expect the state to follow processes strictly. The penalty for failure to do so isn't personal incarceration for the prosecutors or police, but rather failure of their case. This seems like a tradeoff that works in practice.