Really weird, why am I not experiencing these same issues?
Does this have something to do with ticks vs samples mode for your tracks?
I will say since I don't always quantize all my parts, I've gotten into the habit of using an offset when I cut & paste (so I will often select a region 1/16th note earlier on both the start and the end than what I want to duplicate, so that any note beginnings that fall before the beat are selected.)
I have NEVER experienced random sections of MIDI getting messed up from cut and paste, not once in 20 years of using ProTools. This is over thousands and thousands of MIDI tracks.