So then why wouldn't you do that all the time then?
This is an excellent question. Mostly because the answer isn't technical.
I am a man of science. I usually let facts, testing, and knowledge dictate what I do. I could never find any of that for parting upside down. Just many examples of people successfully doing it especially on smaller lathes.
Therefore, I mostly only do it because I have to and I almost always try to do it conventionally first. So it's somewhat more of a practical answer than a science one. If I could get my head around the science, I'd prolly feel differently.
The other piece of the answer is somewhat emotional. It feels uncomfortable to do it that way. Almost everyone does it conventionally. I don't like to be different. It feels uncomfortable to be so different. If it were really so much better, everyone else would do it too. But they don't. Why not? Your question could easily be asked differently - if it works so well, why doesn't everyone do it that way?
With your question as my motivation, I'd like to explore the process a bit more. Please forgive the lengthy discussion - or just stop reading here.
The reason that parting upside down works is mostly geometry.
With regular parting, the cutting tip can grab and can get pulled into the part - the resulting chatter and damage can be catastrophic. The other possible result is failure to cut at all. It just starts squealing against a part that becomes work hardened to the point that even a hack saw won't cut it. Then the only way to make progress is to do side cuts to expose new material and then progress in side-to-side steps. Yuk.
"I think" that the reason that parting upside down works so reliably is because it is more like using a hack saw. If the tip doesn't cut, it just bounces, or cuts a wee bit at a time till it finally gets enough bite to cut.
The reason for this is the geometry. An upside down tool bit doesn't get pulled into the work when it cuts, it just lifts up and away from the part. "I think" this is a bit analogous to the climb VS conventional milling situation where some backlash can allow a bit to "dig in" during climb milling with bad outcomes.
My main objection to parting upside down is probably my concern for the way that the saddle, cross slide, and compound are tied down. Normal parting exerts a downward compressive force on all the parts of the tool holding system against the bed. But upside down parting is trying to pull them apart. The system is designed to handle compressive forces with strong solid flat surfaces, not tensile forces trying to pull everything apart. I just don't know enough about how that all translates to the parts of the lathe so I am reluctant to do it unless I have to. That said, it has never been a problem and has always worked when other methods don't.
In summary, I am a chicken and I prefer to do what everyone else does. I only venture into unknown territory when I have no other viable choice. Hopefully I never have a problem and maybe in time I'll end up always doing it that way.
Prolly more said there than needed but at least I tried to answer a very worthy question. Thanks for asking it and making me think about it more than I would have otherwise.