The theory: Evidence is gathered, a warrant is issued upon probable cause; you are arrested, held in jail for a short while until you are tried by a jury of your peers and found guilty or not guilty.
The reality: Arrests are more commonly made because the subject talks and gives away something incriminating, or has incriminating evidence on his person or in his home, or is ratted out by someone. Not a lot of Columbo or Murder, She Wrote detective work involved (nor CSI in most cases). Many get out on bond. Most use a public "defender" and plead guilty in return for a reduced sentence... that's assuming some pre-trial intervention doesn't occur resulting in probation or whatever. If you insist on a jury trial, it will probably take at least 1 year, perhaps 2 or 3, to go to court. If you can't get out on bond, oh well you sit in jail. ("Speedy" trial? Define speedy...)
If you insist on a jury trial, the solicitor will be most reluctant to pursue one (they are expensive and very time consuming, and we don't have nearly enough courts to try all cases if everyone insisted on a jury trial), unless he is very nearly certain he can get a conviction. Now, once a while he will misjudge it and someone will walk, but most jury trials do end in conviction, and in punishment for making them go to all that bother they will probably give you a stiff sentence, like the maximum.
The reality is that not many REALLY INNOCENT people reach the point of a jury trial. Some, yes... but the percentage is certainly small.
If you actually go through all that and are found not guilty, I can see making the State reimburse you for lost time/earnings while in jail, legal fees and so forth. After all, a "speedy trial" these days is a YEAR OR TWO. Can you imagine knowing that you're innocent and sitting in jail for two years because you were denied bond? Pretty horrible idea. Imagine you have small children while all this is going on; imagine your mortgage is foreclosed while you're not earning.
As for making cops pay for any kind of erroneous arrest out of their pockets.... basically you'd end up with cops refusing to arrest anybody without a signed confession and a bloody murder weapon AND a witness. Most cops don't make a lot of money and one such erroneous arrest would pretty much wipe them out financially. If you want anarchy and chaos by all means go ahead....