Some years ago I took part in an evaluation of pilots fatigue on short haul by DERA - now Qinetiq.
It seemed well understood, at the time, that towards the end of the third early duty performance was dropping off.
Now, a very complicated topic. My guess is that it would only be possible to improve upon that situation if there were a set of very robust controls governing the pilots roster. In my experience of airline flying these are very difficult to achieve. The problem being that the commercial culture of an airline is to exploit any situation for financial gain and operate to the limit of any controls.
Another issue is that everyone is different and our circumstances change. E.g. I used to hate early starts with a vengeance. However, now that I have a young family early starts are the norm!
Yes, it might be that 5 early starts is less fatiguing than 3 early starts followed by a switch to lates. The issue, however, is not about comparing the level of fatigue between different patterns.
It is about avoiding any kind of fatigue whatsoever.
A more rational approach would be to isolate the early roster entirely. I.e. 2 days off, 3 earlies, then days off. The public would be well protected in this case.
Now, given the aggressive commercial airline ethos a political view might be that, to safeguard cheap flights, the public are happy with the overall level of risk in aviation. Major hull losses are (not yet anyway) a local European issue.
So, the CAA can take a few liberties with pilot fatigue here and there and nobody will shout too loudly.
For the time being anyway.