I think at the very least there should be some kind of juror training process. You'd still tap people from the general public, but these people could maybe serve up to 5 year terms where being a juror is their full time job for that time period, they're trained in advance, they go through some kind of testing period, maybe shadow a couple other juries, and then they go on to serve on real juries. Obviously this would be a paid position much like a postal employee.
Besides being extremely disruptive to jurors' lives, you also have many of the same problems of an all-judge system (people becoming too close to prosecutors and wanting to the rule the "right" way, etc.) without the mitigation provided by the bar and full legal training.
Seemingly free and "just" governments have done much more "disruptive" things in the past, so there is precedent. E.g. Conscription and mandatory military training.
I'm a Libertarian, so I'd say No. But my point was that government has in the past done things that have been highly disruptive to their citizens' time.