The Church doesn’t necessarily prevent it. 500 years ago, she suppressed myriad other localized rites at Trent and replaced them all with the universal Roman Rite. In the modern age, the Church is bringing back many forms of worship thought to be dead. The Dominicans, for example, are permitted again to celebrate the Dominican Rite. The 1962 Missal has been re-authorized (by some reckoning it was never suppressed at all) as the Extraordinary Form of the Roman Rite.
The Anglican case is a very special one, in that the Apostolic Constitution Anglicanorum Coetibus specified the particular manner in which Anglicans can be reunited en masse to the Latin Catholic Church. Their form of worship in the Book of Common Prayer is not a distinct Rite, but considered a “Use” of the Roman Rite, in that it diverged from the Tridentine Mass and was translated into English during the time of the Reformation.
It is entirely possible that other Western Protestant ecclesial communities seeking corporate reunion with the Catholic Church could be offered their own Ordinariate structure as well as granted a liturgical practice to match their own patrimony. It just happens that the Anglicans are the first such Protestants to be offered this structure, and they happen to have a fully liturgical practice that is easily adaptable to Catholicism.
22 Eastern Catholic Churches were permitted to keep their own theology and liturgical praxis while returning to communion with Rome. (Some never left communion.) In modern times, the creation of completely new Rites and distinct liturgical traditions doesn’t happen very often. So we will not frequently see a situation such as happened with the Anglican Ordinariates. But it is not entirely ruled other, either.