I think this comes down to three issues rotations, chemistry, and execution.
I blame Doc for the rotation issues. I don't think he's maximizing the roster he has - I don't know enough to say if trying something strange (the extreme being something like using Pierce off the bench in a Manu role and the less extreme being starting BBD and KG, to minimize the minutes where neither KG or JO is on the floor) would just backfire, but I think some small tweaks could keep the team more effective. Examples - lineup Ray Allen's minutes so he always plays with Rondo. Lineup Rondo's and Pierce's rest periods so one of them is always on the floor. As an outsider, it seems like the roster is more talented and Doc needs to put it together a bit differently to make it work.
I blame the DA and outside circumstances for the chemistry issues: guys being injured for the whole year (West, Shaq, JO) is probably beyond his control (although you sorta expect that with at least one of the three when they have those histories), and trading at the deadline to shake up the top 9 didn't help. (On the other hand, RR, RA, PP, KG, BBD are getting the most minutes and have played together forever, West and JO though injured have been here all year.) Either way this cannot be fixed now.
I blame execution on the players Green, BBD, West are all under performing their abilities (while BBD is probably right where he should be, but he's under performing his reputation.) Mostly this can be seen when West and Green don't take wide open shots they should, or when Baby continues to launch shots he misses. A "true PG" is usually code for someone who can: 1. bring the ball up, 2. run the offense, 3. get guys their shots. When Green and West are passing up open shots and BBD is missing open shots - I don't see how a true PG off the bench will help things. (Caveat unless that PG off the bench ran a great fast break, but I don't think this C's team runs that well with Rondo, so I don't see that changing with a bench PG in.)