Er, no. Since the advent of VHF car radios 20 years or so ago most broadcast sites, main and relay, have been changed to 'mixed' polarisation - in effect diagonal - so that they have both vertical and horizontal components. Admittedly there are a few with very specific in-fill that have horizontal in one direction and vertical in another.
The only disadvantage of vertical polarisation - which is why it was not orginally used - is susceptability to electrical interference. However given the significantly increased sensitivity of modern receivers (giving limiting at much smaller signals) and the considerably lower radiated noise of cars, appliances, etc., it is no longer a problem.