Response-by-mail, yes, though the latency is a drag.
Phone support might have been an option. Even if household phones were rare, most people could get to a location which had a phone. However 1-800 (toll-free) lines didn't exist yet (though you could reverse charges with operator assistance). Hrm ... I'd heard a tale that 800 toll-free service began as the result of a request from President Ford for some way for the White House to accept calls from citizens, though Wikipedia's history of toll-free service doesn't make any mention, might just be a red herring.
More to the point: the idea of individually staffing offices is now pretty much a non-starter. Though I wonder what the real economics are compared with creating a national-scale Web infrastructure.
When Social Security rolled out, there wasn't any other choice. (Well, paper mail.)