Jaybird, I thought that was very appropriate and sensitive what your T did with the other client that you knew.
For me, though, I don't know T's other clients. I am not bothered by seeing the clients before and after me--I even kind of like it. I like that my T has a lot other clients as it means he must be good! I also feel some kinship with them, as we all share this very special T. I feel
well-disposed toward them, if that makes sense. I have never felt that my T's ability to give me everything he does is impacted by his other clients. He has enough for all of us. I trust him to not add too many clients to his load so that he becomes overwhelmed. The thing I don't like about his client load is that sometimes I think it is too big, as it prevents me from scheduling the next appointment as soon as I would like. I've seen it suggested that if you are OK with the other clients it means you don't feel strongly about your T or are not attached, but this is not the case with me. I have a strong bond with my T and we are super close.
That said, once my T was talking to me about a little house he was thinking of buying, especially for therapy--like an office-house. He wouldn't live there. He told me one nice feature is that the room for therapy has two doors so that clients would enter by one door and leave by another. That meant clients wouldn't get to see each other. I didn't think this was good, as I like seeing T's other clients! But clearly he has some clients who don't like this or he wouldn't think this was a good feature. I am glad he didn't end up buying that house.
A few times my T has double booked a number of times by accident and both of us ended up waiting in his waiting room for the same appointment. I've always talked with these other clients and found them to be good people. Not awful, or cringeworthy, or jealousy-provoking. The exception was the last time this happened, I had had 3 weeks between appts and was really feeling like I needed to see him for something difficult happening in my life. And there was this other couple I had to wait with for the same appointment. I just had this bad feeling he would choose them instead of me to see. I told them a couple of times that they would probably get the appointment and then I would have to wait another couple of weeks--arrggh. And how it was so hard for me to get an appointment because of my schedule and I had purposefully scheduled at this time because it was the only day of the week I could see him. I rattled on in a completely inappropriate way. It's embarrassing now to recall. Usually I am very polite and circumspect. I think I was just so near the edge with the stress in my life, that my social skills went out the window.

T must have somehow figured out I needed him that day, as he chose me to see.
It's a very interesting topic and I think can give one a lot of mileage if discussed in therapy.