> Based on historical data, how accurate would it be to say that a recession happens every 7-10 years?

Starting with the Great Recession and working backwards to and including the Great Depression, the gap from the previous US recession for each recession has been:

  6y, 1 m
  10y
  7y, 8m
  1y
  4y, 10m
  3y
  8y, 10m
  2y
  3y, 3m
  3y, 9m
  3y, 1m
  6y, 8m
  4y, 2m
  1y, 9m

Only 3 of 14 of those gaps were in the 7-10 year range, and all of the rest are shorter.