While I favor body cameras, I don't think your reasoning here holds up. Even if we assume cops only favor their own safety and power, we would expect to see this policy around high speed chases - they are dangerous for the cops as well.
"They are dangerous for the cops as well" - That's true..but hasn't it always been true? Car speeds haven't meaningfully changed in the last 40-50 years, so it's likely that the danger to civilians and police hasn't particularly changed either. So, if it's true that police agencies are encouraging less dangerous means of achieving the same ends, why now and not before? The change suggests some other factor, and my supposition is that widespread video footage of these chases may have played a role.
Eh, maybe. I think decisions need less explanation when they're the right one. Why now? Maybe they just figured it out. Hanlon's razer, &c.
If we need to explain "why now", that's still a question with your hypothesis - high speed chases have been dangerous for a long time, but they have also regularly been filmed for some while now.