I dug mine with a small backhoe. As I said, you need to get below frost, and 2-1/2 feet won't do it. The other advantage is the extra width of the hole gives you some fudge room when setting the posts so you can get the building square and the centers precise.

As for treated lumber rotting in the ground, when I built my new barn, I tore down a "temporary" shed that had been there for 15 years. The PT 4x4 that came out of the ground looked like new, and I re-used them on the ell of the new barn.

I think the screened gravel and resultant drainage helped there, but I don't have a baseline to compare to.

Trying to make up for a post hole that's too shallow by pouring concrete around the post just makes the problem worse. If it wasn't under a snowdrift right now, I'd get a picture of a deck my neighbor built. He put 4x4's down about two feet and poured concrete around all of them. It's heaved so bad, it's nearly torn itself off the house.