When I went to the one under the red steps in TS, they said there is "a seat in row C" from memory. No specific seat, but the row was mentioned, and the price. That was good enough for me.

I rarely use TKTS, but the last time I did, I was able to choose my seats - perhaps because they weren't busy.

Whether or not you get to choose your sets depends mainly on how busy they are. I don't think they have seating charts available so all you have to go with, if at all, is a descriptive of row & seat. The issue with that is that different theaters have different seating arrangement so for example, row C can be the 3rd row or the 8th row. If you want to choose seats for sure, you need to go to the discount parts of Broadway Box. Playbill or TheaterMania where you click on seats that are shown on a seating chart.

In my experience, they don't let you choose in the sense that they show you a chart and let you pick. They will say something like "they are in row c right." If you say something like "is that all?" they may offer you something else, but there is no guarantee. So it's sort of halfway between going and choosing them at the box office and going on TDF (where you know nothing until you get to the box office and are handed your tix, which cannot be changed). It pays to know something about the theater(s) where the show(s) you want are, so you can make a quick decision.

I suppose, if you have a smartphone, you could look up the seat on the show's website but the folks at TKTS (with good reason) will not let you just stand around while you look up seats if what they offer is not to your liking & you stand there not moving trying to make up your mind. There's probably a bunch of folks in back of you that will start grumbling loudly if you take too long to purchase.

TKTS is not for those who are indecisive or very particular.

Do not even THINK of looking up seats on phone, calling someone for advice, etc. Actually, you should probably just turn phone off during this transaction, if for no other reason than maybe being tempted to answer if someone calls you. I believe I have seen at least one box office with a sign to this effect -- that is, if you want to discuss with someone, you have to go away and when you come back you go to end of line.

It's bad enough when 3 or 4 people go to box office or TKTS together and stand there discussing while others are waiting.

I agree. That's why I said that the TKTS booth is not for the particular or indecisive. You need to have some idea of what you want to see & where you definitely don't want to sit when you get up to the window.

The discount in advance sites do let you choose your seat

Yes the discount in advance sites (aka coupons) let you select your seat; however, in my experience it is a more limited selection than is available at box office (and I realize people from far away may not have option of going to box office).