That's not correct. That's the opposite of the correct reason.

Consider a simple (not-exactly-Poisson) set of blocks: 20x1minute intervals, plus 1x10minute interval. The average interval size is (20x1min + 1x10min)/21 = ~1.4min

A random moment in time is twice as likely to be in a fast blocks as in the slow blocks.

But average wait time (given a uniformly random start times) is (20min0.5min + 10min 10min)/30min = 110min^2/30min = ~3.6min.

That per-start-instant average wait time is longer NOT because you are more likely to be in a slow block, but because being in a slow block has a much longer average wait-time than being in any of the fast blocks.