Yeeah. I would think Jason would be more likely to give up vigilantism entirely with Batman dead, since his motivations seemed to be rebellion against Bruce's no-kill rule, or to prove a point, rather than being all that interested in fighting crime for crimefighting's sake. If that makes sense.
I just really get sick of these hyped up in-fighting plots, where you have to someone from a given group or family be the bad guy. In this case Jason, or Dick in the Beechen Batgirl mini.