As long as a Priest is competent, and has permission from the Bishop, the idea sounds, well... sound!
The concept of 'rite' also, sometimes, while useful for categorization purposes of liturgiologist, and such, can be oftentimes to 'confining'; in other words, the ideal for the Church should be the bishop, and he has priests under his omophor who use whatever approved Orthodox rites as practiced by the saints of the Church. As long as people don't seek to promote the idea of 'sui generis' churches that have overlapping bishops and such, for each 'rite', then people should be in good shape as far as that goes.
The other issues might be confusion. If a parish or mission is primarily composed of people used to the 'Eastern rite', but, the priest just wishes, willy nilly, to use 'Western rite' one Sunday, or such, that can cause major, major problems; and, to be frank, vice versa. Stability is necessary, while all the Liturgies of the Church are good, all good things must be in order.