A growing squash inhibits further growth, however once that squash is mature and no longer pulling nutients from the vine, others may set if the vine is healthy. The danger in pulling too early is that the squash is not finished, will not cure properly, and will not store well.

I usually harvest them late. But I think that we can judge if it is mature or not by the color of the squash. My experience is that they can continue to mature indoor and I wait until they change color before I eat them (e.g. Sweet dumplings and Acorn squashes tend to be sweeter when slightly orange). But some other squash, e.g. shark fin, winter melon, may taste better right after they are taken from the vine (these are white flesh squashes. If not eaten soon, they last forever).

I'm not sure I agree with the point that pulling it too early, will result in it not storing well. I have had very few squash spoil. I have had many store 8-12 months before eating them and I had one that I ate at the ripe old age of 16 months and it was just fine (I label all my squash with the date they were picked).

I just ate one that was picked last August and grown from a Buttercup that was hand pollinated with a pumpkin flower (ButterPump) . I didn't think it would last because it looked like a pumpkin and was fairly thin, but again it was just fine.

I also still have about 4-5 Triamble that were picked last summer although these guys are so solid with such hard skin that I think they would last near forever!

Seems like a fair amount of data indicating picking early doesn't adversely affect how they store. My daughter thinks I should perform a taste test experiment but I think I'll just continue cutting them when I decide they're done.