Learning, good questions and thanks! And I love that you've had Ts who've offered out of session contact per se, no strings attached - and while you might not have felt comfortable enough with them initially, as you say, the offer itself means something positive.
Unfortunately I have spoken with T about this - several times - his way of explaining it is that during the hour we are together, he is totally there for me, in his words 'anything goes', but the trade off for that willingness to be totally present and accept whatever I bring in (anger included - which is important to me) is his keeping the rest of his life quite separate from therapy. I do get that and hope that in the long run making do with the one (miserable not enough hardly conducive to attaching lol) hour a week will be therapeutic in its own way.
He certainly is worth staying with, and I suppose he's good (compared to the umpteen previous Ts I've seen) precisely because he has this sort of boundary? I am working subtlely on getting a second weekly session, but I think I'm on a hiding to nothing there too

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I also hear your very good suggestion of talking to him about my feelings about this, that's sort of on my 'list of difficult things I ought to but don't want to bring up in therapy'. Opens up big cans of worms

Skyblue, I know I'd feel like you do here, but as I don't have that option, I need to find a way to live with it and get the most from therapy despite really wanting that.
Thanks everyone for your comments on this thread, it's been really helpful and very interesting