The other argument that would have answered the self reporting point, is that the APT rules go far beyond fixing the self reporting issue.Yes precisely. It is self reporting in the sense that any company that enters into any RPT will self report , but as you say it’s not a concept that is specific to football.
And in almost every other field of human endeavour it appears to work.
So, if there were legitimate concerns about under reporting of RPTs due to self reporting (the PLs primary case), then the answer is for the transactions to be declared to the league and for the league to consider if they believed (with evidence and professional confirmation) the parties to be RPTs. On the PLs own line of argument, that would have been the proportionate scheme to fix the deficiency without going beyond what was necessary.
But they did go quite considerably beyond that potential fix to self reporting by coming up with a much wider test capturing far more entities, the APT definition and the whole "before the event" APT regime.