only part of the solution
Last week I had the 'pleasure' of the full body scan in Amsterdam, the scanner operator was quite happy to show me the results, a slightly blurred image that pinpointed my watch I had failed to remove. It was no hassle. I did not feel it intrusive.
However, at the same time there were airport workers bypassing the system, presumably because they were 'authorised'.
Scanning is just one part of the solution, the vetting of airport staff is another, and of course profiling is another part.
If someone objected to a body scan on my flight, then it's him or me on the flight, I would refuse to travel with that individual.