There is NO PROBLEM for the Tibetan Culture to flourish in China, to be recognized, to be respected and to be supported by the Chinese government.
But there is a problem for China to deal with a person that has the capacity to "counter-power" the authority in place in China, someone that may be able to gather people and create opposition and therefore possibly trouble.
The issue that China has is not with the Tibetan culture, not with the religion, it is with the power that one man, the Dalai Lama, has.
This would be true in any other country actually, it is not typical to China.
For as long as the "Tibetan cause" (*) goes, and as long as its "champion: is the Dalai lama, there will no progress possible. China does not like "counter-powers", neither does any government find it welcome.
A government must govern, and must show result quickly and efficaciously.
When counter power are to be dealt with as lobbies or groups, such as syndicates, or a consortium of business interests, it is something that can be dealt with, but when it comes to deal with individuals with great "media" power, it more risky for them, in the sense that it is hardly reliable.
Sorry for those that see the Dalai lama as an enlightened being, but I don't think the government of China sees the Dalai lama as such, they see him as a threat to social stability and therefore progress, so they keep him away geographically, and also they want the Tibetans in China to not rely upon him, they rather know that devotees rely on spiritual figures that do not come with a political baggage.
(*) to my point of view, there is no more Tibetan cause, or only a romantic one that is not in line with the reality as we can see now that in China, the Tibetan culture has been given room to exist and co-exist with other Chinese cultures, it is even sponsored, promoted and protected by the Chinese government.
So I have no worries about Tibet becoming more and more a great place to be for all Tibetans actually, and when i say Tibet, i also mean China.