Good thing we are getting rid of the Coyote's and converting/replacing all the LAV 3 to LAV 6 standards. TAPV replaces 2 vehicles in the Coyote and RG-31 (and some of the Cougars I think). I don't know if the Bison ambulance and Command variants are staying in the fleet. I assume so. But a Bison Amb is much easier and cheaper to run then a full LAV from what I understand and I haven't heard of a LAV ambulance yet (maybe we have one or maybe we are getting them).
Also don't forget the entire TLAV fleet. Really when you think about it discounting the specialist engineering vehicles (Husky, Cougar etc...) The army will have 4 main armoured vehicles. LAV 6, TAPV, TLAV and Leopard. There are a few "micro" fleets but every army has those because you just can't common hull everything.
As for the rest of your post, yah I agree, purchases should match doctrine. In this case though I think the TAPV purchase matched experience.
If we had of had these in Afghanistan there probably would have been more lives saved on the roads. TAPV could have done convoy escort, moved VIP's around, provided vehicles for CIMIC, POMLET, OMLET and PSYOPS teams. It would have replaced RG's and freed up LAV 3, LAV LORIT and in some cases TLAV's to do other work more suited to their vehicle than tooling around Kandahar city moving DFAIT pers to meetings with the mayor.
There were full infantry platoons outfitted with RG's in theatre. In my direct experience the PRT Commander and General Vance's TAC were rolling in RG's as LAV's were needed to fight the war in the nasty places like Panjwai. NSE would have loved TAPV for their escort duties, and probably so would have the Route Survey crew instead of the Cougar "battle buses" they used to protect the Husky VMMD and Buffalo.
So yah, seems like a mismatch for a lot of tasks that we might be trying to fit it into, but it's going to be a good vehicle for so many others that we completely forgot, discounted, discovered or didn't remember were important. The infantry get the TAPV because lots of these tasks are ones the infantry will be assigned despite the fact that lots of these organizations didn't quite fit into the tradition brigade "doctrine".