To be honest, any pilot SHOULD teach certain things to his/herself. That's what makes a good pilot, always coming back to yourself and thinking where you could improve. I do this even if I haven't flown so I feel I'm prepared for a lot of things. A couple of these things, comms and precautionary landing, are things any decent PPL wanting to get a CPL will be practicing on a regular basis, amongst other things like PFL, stalls etc.
But some pilots are just lazy and don't care and this is where I feel structured hour building should still be a form of training rather than exercising license privileges. Hour building should be a time where you perfect precautionary landings, xwind landings, stalls etc and therefore the CPL training can be used to focus on purely the CPL syllabus rather than re-learning what you should know as a PPL.
I agree with some of the things you suggested that should be brought in, such as spinning and learning how to keep weight off a wheel if you don't think it's locked down. But things like comms failure and precautionary field is what any good pilot should practice himself or run it through his head where practice is impractical (comms failure). But obviously that is too much to ask because some people just don't care.
Perhaps a pre-CPL training skills test should be done at the end of hour building. Then you'll be able to filter out the idiot pilots and keep the ones who want to be good. But that won't happen, schools and CAA will lose out on cash. So if half of hour building could be done by guidance of an instructor but still P1 then a lot of pilots will be more curent and fresh with things they did in the PPL so it doesn't need to be brought back into the CPL.
What is more shocking is that PPLs are most flight schools aren't given a POH for their aircraft. Image Mr. 45hr PPL, they would have no clue what to do if oil pressure hit zero and the temperature went sky high. There's no emphasis on knowing what to do when on rare conditions in the PPL. Every pilot should own a copy of their a/c POH and know it. But that doesn't seem to be the attitude. Many engine fires on start over winter at my school due to over-priming, most qualified PPLs jumped out straight away, should they have read the POH they'd have known to keep trying to start the engine for a few minutes.
In summary, I agree overall. Better training is necessary, but it shouldn't be necessary for most things. Only for spins, gear problems etc. A lot of things though should be taken on the pilots back to practice what he's been taught or should know.