We do have more competition, or at least we have more carriers. That was partially my point. We have one more carrier than you do (although we are much larger). The problem is merely that the competitors don't really compete too much.
Whenever I read Americans complaining about their carrier, there's lots of people saying that they can't switch because only their current carrier has the coverage they need. With good coverage I mean at least 95% of the population being covered by a particular carrier, so the people who can choose between all three are 0.95^3 ~= 86% of the population. In Switzerland all three have >99% coverage of population. Granted, that's much easier than doing it for all of the US, but how about similarly dense areas? In the US there are three metros with more people than Switzerland: New York, LA and Chicago. Note that this comparison is going easy on American carriers, since Switzerland does not have the density of a metropolitan area, and is geographically much more difficult. Do you get a choice of at least three carriers with >99% there?