Great question (and so intelligently asked that I feel like we should all slap on tweed patches and pipes *grin*).
I think you may be on to something about size being an issue of some sort because nobody except GEDmatch quite does what you described. The new DNAgedcom site has tools you can use to make it much easier to do this yourself (without requiring matches at either of the Two Other Companies to join GEDmatch), but it's not quite the same. (Still totally brilliant, though.) Even GEDmatch first shows you the matches on a segment, then makes you query over and over to see if those matches match each other, which can get very tiresome if you have many matches on that segment and you want to check them all against each other.
(Possibly I'm doing it wrong, though. I know about the triangulation tool, but it doesn't show segments and for me it's just page after page after page of head-swimming info, lol. I find it easier for now to just look at specific segments where I have some idea about their origins.)
Anyway, what you describe would be a *tremendously* useful tool, but I think it would require an immense amount of system resources, otherwise surely the other companies would offer it? (Dangerous assumptions...)
Maybe Ancestry could implement it a bit subtly and only by request, with options like the following:
Show me all matches on chromosome [ ] between [ ] and [ ].
___ Refine to show only matches who also match each other.
___ Refine to show only matches who also match each other on this segment.
___ Refine to show only matches in common with [drop down list of other accounts managed by the same person]
Show me all other matches who match this person.
Show me all other matches who match this person on the same segment.
That way we would have to request the information, not have it constantly generated and available (as cool as that would be!)
So, did you run to the Beta Feedback button with this yet? Hehe!