I think that part of the fact that a formula such as (1 RM = 3 RM plus 11%) may work well for many powerlifters, is that if you don’t have that kind of increase from 3RM to 1RM, then you won’t be a decent powerlifter and won’t be trying the formula! For the general population, it will fail for many.
While agreeing with the principle that learning to do maximum singles and building that skill is the only way to arrive at a true 1RM value, a good result for I think practically anyone is obtained by estimating 1RM as equal to 3RM plus the difference between 3RM and 6RM. When the gap between 3RM and 6RM is small, rather consistently the gap between 3RM and 1RM is similarly small also: likewise where the gap of one is large, it rather consistently is large for the other as well. The exception may be if Golgi tendon inhibition limits the 1RM performance. If so, though, in terms of planning training cycles the calculated value, representing an estimate of potential strength ignoring that limitation, probably is a more useful value than the actual one, I would think.