I don't have experience with a tarp tent but have difficulty seeing the point for my purposes. Depending on my type of trip, I gravitate towards one of two solutions:
A. On an extended trip e.g. months or more; I like a more general purpose solution with a few attributes: (a) good shelter from the elements (b) flexibility in how/where I pitch it including freestanding as necessary. In this vein, I took an REI Quarterdome 2+ for an 18-month trip across the Americas and also on a 4 month trip across Africa. I took a Hubba-Hubba for a 10 month trip including across Russia. I found these to be general purpose reliable tents - that while pretty worn after trip of 18 or 6 or 10 months, did the job.
B. On a shorter trip where perhaps a tent isn't my primary shelter, e.g. a week or so trip or a longer trip but with camping more as a backup; I can take something that does basic job of sheltering. Light and inexpensive are two useful attributes and needs to at least handle weather. For this a basic tarp or tube tent can fit the bill.
The tarp tents on that site don't quite fit the bill for either of these points. Either they are essentially enough like a tent - that I can evaluate them as tents - though seem to be on the expensive side. Or they come after my quick shelter idea in which case they seem both heavier and considerably more expensive than a basic shelter.
Hmm. Interesting thoughts.
Of the tents that you can put in your category of a more robust tent - why do you say the Tarptent models closest to that still don't cut the mustard?
Reason I ask, is that, to me, if you add a solid interior the tents seem like regular tents to me. They just make use of lighter support options and/or trekking poles, as opposed to tent poles. So what about their construction or design, to you, makes them not fit?
I can understand the quick/light shelter idea.
The A frame tent I have is pretty small - sort of like the Pro Trail model only it doesn't taper on the far end (either side to side or top down). The reason I haven't used it beyond 1 backpacking trip (it has been on some car camping treks of sorts) is I can't stand bumping the sides in cold weather when condensation has formed. With more ventilation that would be better, and certainly with a proper fly. With that said, a small solo shelter like the Pro Trail - with a good fly - might be a good option to have. Though, it might be hard with that space to hunker down for a day of storms in it.