Public defenders will try your case if you demand trial; in fact, a lot of public defenders probably try more cases than paid attorneys.

The problem is that public defenders generally are starter defense attorneys, they're in the job to get experience so they can eventually quit and take a cushy private role. And secondly, they have very little time to allocate to each case; if the defendant is stuck in jail, then they have even less time to visit the defendant and prepare any kind of useful defense or trial strategy.

A public defender's primary strategy for their client is to, sadly, negotiate the best possible plea deal in the shortest amount of time to get the case off the docket.

(This might actually be in the best interests of the defendant; most defendants are guilty of something in the charging document, even if not everything they've been likely over-charged with; the justice system isn't quite so broken that it scoops up a huge number of factually innocent persons)