My kitchen has been the experiment for several years. I have 5 starters (French, Austrian, Russian, Ischia, and a new Tuscan). I use them all regularly and each has different flavors and fermentation/proofing behavior. If the "local domination" theory were correct, I would have 5 identical cultures.
I generally agree with you about local domination, but I'm not sure it is that simple. I think there are at least three possible scenarios in which a local wild yeast contaminates a particular starter culture:
1. Local Domination:
The local wild yeast is somehow stronger or more aggressive and manages to completely dominate and displace the yeast in the starter culture in which case the starter takes on the characteristics of the local wild yeast.
2. Starter domination:
The yeast in the starter culture somehow prevents the local wild yeast from ever gaining a foothold in which case the starter remains more or less unchanged.
Both the local wild yeast and the starter culture coexist or hybridize in which the starter culture may take on some of the characteristics of the local wild yeast or perhaps even some all new characteristics.
I think scenario #1 is the least likely given everyone's observations (mine included) that no two of our respective cultures have the same set of characteristics. Still it can't be ruled out completely as perhaps only one of our cultures was weak enough to be dominated by the local wild yeast (though we all three have one in common - Ischia).
Perhaps someone has done research to establish that #2 is the most likely, but short of that, I can't think of any reason to assume that it is. The fact that we each have multiple cultures with distinctly different characteristics does not, in itself, establish #2 as correct.
Short of evidence to the contrary, I would lean to #3 as being most likely. I don't know we would assume that local cultures couldn't or wouldn't take up residence in our starter cultures and that even if they did, they would not impart some of their characteristics. Scenario #3 is equally supported by the observations as #2 which only suggests only that there are differences in the cultures - not that the original cultures have not changed over time.
An experiment such as that proposed by sbinder77 - or simply looking at several of the same original culture, taken from different locations, under a microscope - could go a long way toward ruling #2 and #3 in or out.