A famous combination used by the Native Americans was beans, corn, and squash or pumpkin. The corn would provide a a trellis for the beans to climb on. The beans would inject nitrogen into the ground, not in time for this year's crop but helpful for next year's, and both squash and corn use nitrogen. The squash would act as a living mulch, covering the ground and keeping weeds and grass growth down while conserving moisture. I've heard that combination called the three sisters.
The corn was dent corn, harvested dry on the stalk in the fall. The beans were pole beans, harvested after they dried. They were not eaten as green beans. The squash was winter squash. Guess when it was harvested. This little detail of the types of crops originally used is often not mentioned.
I've tried this combination, sort of, but not using the same types of corn or beans as original. My sweet corn is finished and harvested by the time you pick the beans, but the corn stalks do hold the bean vines up. The winter squash vine is underfoot. You have to be very careful where you step in there. As you mentioned, it is hard to harvest. I have not tried it in a raised bed. That may work better. I have not tried summer squash or zucchini because of the compact growth habit. I'm sure others on this forum have tried various combinations and differetn methods. Hopefully they will chime in with their experiences. It would not surprise me at all if someone has done something like this and were very happy with the results.
With that history lesson out of the way so I could point out the different types the original three sisters were, the dent corn, dried beans, and winter squash or pumpkins, your method sounds good. I would not plant all three sisters together because of the difficulty of harvesting, since I grow sweet corn and use beans as greeen beans. But I plant sweet corn and winter squash together to save space. It works well. I have not done it, but I'd expect corn and beans planted together to work very well, just don't have squash underfoot when you are harvesting the green beans.
It would not work for me to plant corn and peas together. I plant my peas as soon as the ground can be worked since they are a cool weather crop. The corn is planted after the ground warms up. The peas would be finished long before the corn was anywhere capable of supporting them. Now, I'm talking about green peas, If you are talking about a different type of peas, that could be different. Sometimes these little details are important.
But its a perfect pairing for when my poles beans need to go in. However, my pole beans are still going when my corn is done. So the stalks end up staying the in the ground to support the beans, so I don't get to use that bed again.
