I genuinely believe sex with a therapist can be very cathartic.
I could not disagree more strongly.
I know society frowns on this because of the power differential
The power issue is part of it.
For many people, their therapist is the first - only - person in their life who truly listens to them. Who accepts them for who they are. Who looks at them with care, and with interest. Who wants to hear what they have to say. Who understands and empathizes.
In short, the therapist is the best first date you ever had, over and over and over again.
The illusion of intimacy is just that - an illusion. What is being developed is called the "therapeutic alliance". This is necessary in therapy - it is the phrase for the bond formed between a therapist and a client, in which they have both tacitly agreed that they are both there for the client's well-being, and will work towards that together.
While this bond is being formed, transference can occur. it's very, very normal. But it's not meant to be acted upon. Those feelings are not grounded in reality. They are based simply on the fact that your therapist makes you their entire focus for a period of time, and that can feel like love.
I do believe there are scenarios where safe touch from a qualified professional could be so healing.
Qualified for what? Sex therapy? Even they don't have sex with their clients; they have their client work with a surrogate.
You absolutely should talk with your therapist about your feelings - either they will become predatory and take advantage of those feelings, in which case you should get out - or, they will explain to you why that's never going to happen, and you will be able to move on.
Unless you are already having sex with your therapist. Then, they aren't your therapist anymore.