My therapist is a like yours. She doesn't like when I ask questions about her, which I think is because sessions are supposed to be focused on the clients. She never gives out her email or allows texting because neither forms of communication can guarantee confidentiality. She also doesn't do physical contact, which I'm incredibly grateful for, because I feel that would be inappropriate, at least for me.

To be honest, I think 90% of therapists are like that. Those that provide more than that are probably rare, because there are some pretty valid confidentiality concerns and boundary concerns that can arise out of allowing email, physical contact, and texting. In any case, evidently there are therapists who offer such things, so you could always interview new ones. But I don't think you're being shortchanged because those things aren't common in therapy.