First, to answer your question, yes, there was a situation once when I asked the therapist to change their style and they didn't, at which point I realized that I needed a different therapist.

In terms of hugs, while your therapist has the right to refuse to hug you, it's not therapeutic just to say no. It would've been much more productive of him to inquire about the reasons why a hug from him is so important to you. Then you would've explained to him the same thing you've explained here and that is you just need to feel like you exist for him. Then the conversation could've developed further into what makes you feel like you exist in general and what makes you feel alive in general, which could've also touched upon your feelings of self-worth or a lack of thereof and so on and so forth..There is so much that your need for a hug could've opened up if your therapist used it as an opportunity for exploration, which doesn't sound like he did. In addition, he could've also tried to explore with you what other things besides hugs would make you feel alive, feel like you exist. This is what therapy work is really about, it's not about enforcing "boundary" by saying no to your wishes just for the sake of the boundary itself. Boundaries and their enforcement don't have any meaning if their purpose is not understood and if they don't help the person understand themselves and their own needs better.

This kind of work might've diminished your need for hugs or it might've not. Sometimes, even when we understand the underlying forces that make us crave certain things, we still need what we need. That is to say that there are cases when people DO need to be hugged and held physically in order to start healing. If this is truly your case (I don't presume to know that) then you'd have to find a therapist who'd be willing to fulfill your request. There are therapists who are willing to hug their clients, who feel comfortable with hugging clients and who absolutely believe that hugs are healing. Now, I do have to say that not every therapist who is willing to hug clients can do it safely without getting into an ethical slippery slope. Making hugs a part of therapy requires the exceptional level of mindfulness on a therapist's part. Very few therapists are on that level. But they do exist.