I suspect there are lots of reasons why one T would allow one type of touch over another, or why they would or wouldn't allow touch at all.

Some of it is probably as simple as client or therapist preference. If a client is very uncomfortable with touch, or if a therapist is uncomfortable with touching clients, then it would not be appropriate to do so.

A therapist might decide that touching a particular client is not therapeutic - based either on that client's history, their diagnosis, or transference issues (or a million other things that a T might consider).

It might not be part of that particular therapist's philosophy, so it's just not something they do. No other reason than that it's not an approach they choose to take,

As for why not a kiss on the cheek vs a hug vs holding hands...I suspect a lot of that is cultural as well as the above reasons. In the US, a kiss on the cheek is not a common form of casual or comforting touch. It's generally reserved for more familial interactions, or interactions between very close friends of the opposite sex. It's not used as a greeting or a goodbye, and would be considered inappropriate in a therapy setting. Holding hands is kind of the same way - it's often considered more something that is done between family (small children with parents) or intimate partners. It's not something that is typically seen in casual interaction. Shaking hands, yes, holding them, not so much. In the US - a hug is generally more of a casual gesture that shows you care about a person. It's more accepted as something that is done between friends, close acquaintances, or even just people wanting to offer comfort to each other.

Honestly, I'd freak if my T wanted to kiss me on the cheek (would feel too "motherly" or "grandmotherly" and I'd have serious issues with that). I'd be uncomfortable if T wanted to hold my hand - would make me feel like a little kid. I'd probably be okay with the occasional hug, but I'm not generally a hugger either.