Defenders are theoretically entitled to speedy trials, but in reality can be held for years and years without trial based on procedural delays, and, in particular, based on the court's scheduling problems:

http://www.newyorker.com/magazine/2014/10/06/law-3

And a huge flood of criminal trials would certainly not make individual criminal trials any more rigorous, or juries any more likely to carefully weigh evidence.

Finally: people on HN royally fucking hate hearing this, but it's true: most criminal defendants are guilty. We hear about newsworthy cases where there's enough of an interesting narrative to write an interesting lede graf. But for every one of those, there are 100 where the details are completely uninteresting: the defendant was found in his living room with bloody knuckles standing next to his unconscious spouse.

A plurality of Cook County inmates are in for domestic violence; the majority are incarcerated for violent crime. So the idea that we'd have a fairer system by ensuring that fewer defendants actually faced charges is... suspect.

The injustices in our criminal law system need to be fixed at their source: the law needs to be changed to ratchet down sentences. This is an uncontroversial point. There is broad agreement that sentences were escalated to untenable levels during the nationwide freak-out over crime from the late 1960s through the mid 1990s. That problem needs to be fixed; no cosmetic change will improve our system until it is.