If think the issue here is "Notifiable Work" rather than "Part P". I personally believe, if the nature of Part P is safety, then all work should be notifiable, simply because ...
As you say, there's absolutely nothing wrong with Part P itself; it merely gives a legal basis for what we all already expect - that electrical work should be done safely. I also have to agree that, in theory, there is little point (in general, not just for the specific reasons you give) in having such a legal requirement unless it is fully policed - which, as you say, in theory would require all work to notifiable. By analogy, there would be no point in having laws (and signs) enforcong speed limits on roads if we then just relied on the fact that everyone would obey those rules, without any 'checks'or 'policing' that they really were.
And with correct I&T and documents to represent/back up this work, and a register to confirm what work was done, then that would make things a lot safer. I know that will never happen ....
As you say, that will never happen. Nor would it necessarily be an answer, unless the system involved widespread third-party inspection/audit.
...but if we are trying to keep things safe what is the alternative?
Probably nothing which is practical. The only 'total solution' would be for all electrical work to be both notifiable and subjected to third-party inspection - which I think would be totally impractical, and undoubtedly far from 'cost-effective'.
One of the problems is getting a handle on the magnitude of the safety issue, which is an essential starting point for deciding what (if anything) we need to do to address it. If we knew that there was a horrendous problem of deaths, injuries and property damage resulting from sub-standard electrical work, then 'we' (society) would have no option other than to introduce some draconian measures - but I really don't think that's the situation.
In practice, we are starved of useful statistics. Anything other than (the tiny number of) deaths due to electricity is very poorly documented - and, even with the deaths, it's imposible to determine how many (if any) had anything to do with unsatisfactory electrical installations. 'Electrical cause' is seemingly used as a scapegoat for fires when no other cause can be found and, in any event, a high proportion of the 'electrical fires' are reported as being due to things other than the electrical installation - e.g. due to appliances, consumer abuses (e.g. 'overloading') or 'putting objects too close to a source of heat'.
All-in-all, we haven't really got any good clue as to how many deaths, injuries and fires are due to problems in electrical installations, nor how many of those that were due to sub-standard installations related to work which had been notified (and self-certified or LABC-certified). It therefore might well be the case that, perhaps contrary to our intuition, 'incidents' related to un-notified electrical work may actually be very rare - and hence perhaps not justifying a complex and expensive 'system' to attempt to reduce such incidents further.
Kind Regards, John