An interesting idea...
...but one that is going to run into minefields.
Firstly, which characters are you going to use? If you use the DMG standards, then Anubis still won't be happy, as this was his original objections. If you don't, then how do you get a 'standard' character of any class.
Secondly, selecting the opponents to go toe-to-toe with is going to be difficult. A very broad spread could be achieved, but it would have to be weighted in favour of 'commonly encountered' monsters. An orc should have a greater 'weighting' than, say, a Ravid. There are added complications with what level to play the scenario at, as this does greatly affect the performance of the classes (e.g. wizard). Surely you don't propose testing a 'basket' of monsters at all levels then taking an average? If so, I'd rather you be doing it than I

.
Thirdly, you have to bear in mind that some classes are stronger than others into the short-term and the long-term. That is why it is difficult to compare the spellcasting classes in a direct comparison with the fighting classes. In a series of three monsters, spellcasters will fare much better than in a series of ten. Again, this will be cause of dispute.
Finally, there is the problem of non-combat abilities. The hapless bard is (rightly) slammed, but part of this is due to their strengths in the non-combat field. Similarly, rogues are strongest in areas outside the straight-up fight. By contrast, the fighter is generally useless outside a combat scenario (discuss...)
So, these four problems, in addition to those you mention (although I'll admit there's an overlap in our reservations) make the task fiendishly difficult and prone to dispute. I'll stick to comparing stat blocks.
PS If you do manage to find a reasonable system (despite the inherent difficulties) then I'd be more than happy to test it.