I think the fundamental issue with the CR system is that it doesn't take it into the PCS themselves, and there is no reason you couldn't do this. For example, just like monsters, you can get the PCs standard AC, HP, you can look at what damage models they use most of the time, and then calculate a CR number for each PC. And then use them as a comparison between monster CR.
Sure its more work, but you at most have to recalculate it one a level, or if the party gets a particularly strong magic item, so its not something you ahve to figure out constantly.