In the standard questionnaire that prospective jurors are given, they are asked if they or members of their immediate family have been victims of a crime, or if they work in law enforcement. Now that felons will be part of the jury pool, they will undoubtedly also ask if they have been convicted of a crime themselves.
In my experience, judges will themselves excuse jurors who have family in law enforcement (parent, spouse, sibling), which means the lawyers don't have to bother using a challenge on it. I would expect the same will happen with many/most criminal convictions, especially when they are related to the crime that is alleged.
And even when they are unrelated, I expect the prosecutor would dig in and ask questions like "have your feelings about respect for the law changed since you were convicted of embezzlement?" — even if it's an assault trial. These questions will be uncomfortable for the potential jurors, who may feel like they're being humiliated and put on trial all over again. I would not want to be a felon being questioned for jury selection by a prosecutor.
note: my experience is in San Mateo county jury selection as a private citizen. I am also a former lawyer, and almost all of my lawyer friends have never made it past jury selection. I served once, only because I emphasized that I practiced tax law, which is very different from criminal law.