I agree with the assertion that the city manager is perhaps the best, if not the most democratic, strategy for running a government, in Texas or elsewhere. That said, however, they are usually not given long contracts, in fact sometimes shorter than the terms of elected officials, and are therefore as subject to politics as actual politicians are, sometimes even more so. Where city politicians are answerable to the electorate for their elected positions, city managers are answerable to city politicians for their livelihoods.
The fourth form of government, by the way, is the town meeting, which, even if the meetings are conducted among elected representatives, is best suited for very small communities. In Texas, I could only see it used in the more remote, rural regions of the western part of the state.