It makes no sense that money police collects goes directly towards funding any government department. It should go into a tax refund pool.
however, i'd challenge the idea that solving more crimes is necessarily a better use of our tax dollars.
cars are the number one killer of people in america that police can directly affect. so why wouldn't we want more enforcement of traffic rules (which is where most of those fines come from), to reduce traffic fatalities? (we need to know which rules best reduce fatalities of course, but that's a given)
suicides are also high on that list. community policing techniques can help there.
and don't get me wrong, homicide investigations are important, for both prevention and justice, but homicides shouldn't dictate spending on, and the attention of, our police force.
at the bottom of the list are mass shootings (basically a rounding error of yearly gun deaths), yet police forces spend disproportionate amounts of money on (reacting to) mass shootings (assault weapons, active shooter gear, tanks, etc.).