Why finding cheating by statistical analysis worries me

Let me be clear.

At heart, I'm a number-geek.  Not a very good one , maybe, but I like being able to measure things.  The idea of turning up cheaters by doing statistical analysis of some kind is, at first, quite appealing.

A number of different methods have been proposed.  Without going into the details of any of them, they can all be pretty much summarized as:

Do a bunch of statistics to determine if any pair's results differ substantially from the average expected result of their peer group, and if so, look into them more carefully.

This has several drawbacks, it seems to me

1. Winning pairs will inevitably have results that differ substantially from the average expected result of their peer group.  That is, even among WC players, winning consistently makes you an outlier.  So why not skip the statistics and just always investigate the winners? (slightly tongue-in-cheek here, but you get my drift).
2. Most of the proposals I've seen assume, at least implicitly, that the peer group is "clean"--that there are no cheaters in the bunch.  And hopefully it is, but there's a chicken and egg problem here.
3. Most importantly, occasionally somebody makes a breakthrough that gives them a competitive advantage.  I'm not well enough versed in the history of bridge theory to cite a real example, but hypothetically, let's say that the Law of Total Tricks was such a breakthrough.  Until it was popularized, pairs that had figured out the Law, or that had figured out something analogous to it, would have had a competitive advantage--one that might well have made their results stick out, relative to their peers.  ("How did he know not to take that sacrifice?" "He must be cheating").  One assumes that most such breakthroughs have already occurred, but how can we know?  The best suggestion we get in such cases is that players who make choices that the current top technicians would avoid will need to be able to explain why they did it.  But that puts them in the position of either giving away their hard-found discovery, lying, or, by not being "word" people, being inarticulate.

Basically, it seems to me that most of the "find cheaters with statistics" schemes amount to "investigate people for winning."  And maybe we should do that, just as the medalists at the Olympics pretty much always get selected for closer inspection for doping.  But let's not waste a lot of time pretending we're doing anything more significant.

(Note:  Some of Kit Woolsey's preliminary work, in which he uses statistics to try to help identify hands that might be worthy of further scrutiny, strikes me as valuable.  And I'm all for developing as complete a statistical picture of what "good bridge" looks like.  I just think we're better off using statistics to help understand the game better, not to tag people as potential cheats because they are successful).