The curse of pathology training is that at few to zero points are you allowed to completely be The One with simply the "option" of calling your attending. Most other residencies allow greater actionable responsibility -- not only formulating but implementing a course of action, with all its ups and downs. I particularly enjoyed and I think learned the most on a long rural rotation during a year of clinical internship, largely because of the relative autonomy I was afforded. Unfortunately, lack of need combined with inability to bill for much of what a pathology resident might otherwise sign out means many programs have no great system for increasing the responsibility of even final year residents. The good programs find a way to do this to some extent, but systematically it's just not that great. I don't think it's a problem of never learning how to sign X, Y, or Z out, it's a problem of never getting a chance to really do so on one's own until AFTER residency. For some that equals a lack of confidence..but not necessarily a lack of competence per se.
Personally, I do think the CP disciplines should have appropriate pathologist oversight. However, because very little has a billing component requiring a pathologist, the trend has been that pathologists leave day-to-day activities to senior techs...which doesn't really bode well for maintaining competent authority over the lab, much less communicating intelligently with clinicians who may need questions answered, going forward.
I'm not entirely sure what you mean by the "good" parts of CP -- any CP discipline could have heavy pathologist involvement, but most don't require it. They are all pretty technician dependent. I've seen micro labs where the director was in there every day helping out or tracking certain cases, and others where that was decidedly not the case. As for the CP boards.. I don't think they're necessarily difficult, merely that most programs train only as much as their CP pathologists/PhD's work, which may not be a lot. When residents almost universally indicate they have a lot of free time on CP, this indicates to me they're simply not being trained (nor, by extension, being prepared for the CP boards).