Derald wrote:

... and it seems to me the legumes would be
putting nitrogen into the soil to late in the life cycle to be of any short-term
benefit to their companions.

The cycle goes on for many years so the nitrogen from the legume applies
to next year's planting. Whether it's enough when planting all three
together is an interesting question. It's certainly a better sitution
than planting corn and/or squash year after year in the same location.