In my experience, they do, but they're marketed as luxury housing so the stigma isn't as apparent to your typical person who is sympathetic to NIMBYism.
Townhomes are seen in large numbers in the form of townhome developments i.e. pave a parking lot off a major road and throw up several rows of townhomes in it. What is less often permitted is for an existing city grid to have a mix of single-family and townhomes, or for older single-family homes to be replaced by townhomes as an area becomes more in demand.
Here in Florida they're not "seen in large numbers", they're dwarfed by the ordinary suburban single-family dwellings, both already built, and new developments going up like wildfire. Every other form of housing combined is dwarfed by them.
