The principle of "innocent until proven guilty" means that there should be quite a few dangerous people out there
This is a bit of a false dichotomy. Democratic law enforcement does not hinder the overall quality of law enforcement. Just look at the US, where over the last 30 years, all liberal protections of law have been more or less whittled away to optional, has done little to keep criminals off the streets. Guilty until proven innocent prevents false convictions, which actually helps keeping dangerous people off the streets, because a false conviction closes the case and lets a guilty man walk free(in addition to incarcerating an innocent one).
Even if it did work like this, its a small price to pay to keep institutionalized abusive behavior from happening, if the price is only a handful of petty crimes. Or think about it this way. The police shoot and kill more people every year that all spree shooters did between 1985 and 2015. Most of the really bad abuse behavior done in the USA is done by policians, cops, corporations and their representatives, and other authority figures.
The wierd way that people complain about the state not protcecting them at the same time as trying to talk away all regulation power from the state shows some kind of really strong mental dissonance.
I think the wierd way you confuse "unlimited police powers", with "unlimited police abilities", as if people complaining about police abuse don't want the police to do their legtimate jobs. So your point is a strawman.