"The county of Suffolk seems to be home to countless examples of these crinkle crankle walls. On freston.net you can find 100 wavy walls that have been documented and photographed."
Although it's not explicitly said, let's suppose that every one of those wavy walls is in Suffolk. The population of the county is 761 350 - let's assume there are 100 000 homes (although there is the city of Ipswitch, it's otherwise largely a rural county where single-family homes will be common). So only roughly one-in-one-thousand homes in Suffolk has such a 'wavy wall'. Elsewhere in the country probably even less - e.g. I've never seem one.
Any for everyone complaining about mowing - do you actually have grass all the way up to your boundary wall? In my experience it's pretty common to have a flower bed running all the length of the boundary, so mowing would not be a problem.