Yes, you’ll get the alternating pile phenomenon more and more often. In reality, big “clumps” of cards from one pile or the other actually improve the randomization. In the extreme, this becomes the Faro shuffle https://en.m.wikipedia.org/wiki/Faro_shuffle
From a probabilistic standpoint, even if it isn’t a perfect Faro shuffle, almost-Faro shuffling clearly introduces far fewer bits of entropy which is less than ideal.
I wish! Yes, the better you get at riffle shuffling, the more it will approximate a faro shuffle (meaning less "clumps" and more singles alternating) in some parts of the deck, but it's the repetition that makes it random. If you have accidentally mastered a perfect tabled faro without deliberate practice, I'd like to shake your hand and read your book (or video) on the technique!
Perhaps we can caveat that the person is not cutting perfectly at 26 every time and performing perfect out faros, then we can assume they'll be mixed enough. :-)
It's been a while since I've read Persi Diaconis' paper (who coined the 7 shuffles thing), but I believe all your main concerns were addressed. Not sure about the sleeved deck thing, that wasn't probably a consideration.
From a probabilistic standpoint, even if it isn’t a perfect Faro shuffle, almost-Faro shuffling clearly introduces far fewer bits of entropy which is less than ideal.