Of course they do want the independence, why would they not. It's just that after decades of occupation and China's economic rise, they feel that that is an impossible goal, at least until China implodes like the USSR did - which may or may not ever happen.
So, they are asking for the next best option as a compromise - even the proposal is called middle-way for it is a compromise.
There are benefits to being associated with a global superpower in regards to quality of life improvements. Obviously they are not worth the cultural and human costs that Tibet is currently experiencing, but if we can get true autonomy, I don't see why you wouldn't want both. I say that as a Tibetan in exile.
There are some Tibetans that don't think true autonomy is possible with the CCP and thus still want independence though.
So, they are asking for the next best option as a compromise - even the proposal is called middle-way for it is a compromise.