As far as the U.S....
In some company schools, young ballet dancers do get encouraged to try their hand at choreography.
At SAB, there is a choreography project for students in the intermediate and advanced levels: http://www.sab.org/choreographyprojects.htm
To quote from the website:
Each fall, students are invited to apply as choreographers. Selected students consult with SAB's music instructor on their music selections and select up to four dancers from SAB's Advanced Division on whom they will choreograph a short ballet. Student choreographers are allotted studio rehearsal time over a two week period, culminating in a series of performances in a workshop setting for faculty, staff, fellow students, parents and friends of the School.
Several students have also participated in the NY Choreographic Institute, a program which also helps to nuture budding and emerging ballet choreographers. The alumni of this program include some of the big young names in choreography - Christopher Wheeldon, Alexei Ratmansky etc. SAB students participate as dancers in the Spring sessions.
I don't know about programs at other companies, though given the number of dancer-choreographers at the San Fransisco Ballet and Pennsylvania Ballet, I'd assume they have some sort of program. Miami City Ballet has also provided opportunities for young choreographers.
My impression is that dancers like the ones at SAB may do some choreography in school, but that it gets set aside for at leaast the first few seasons in a professional company due to time and energy constraints. It's not until they have a more secure and comfortable position in the company that they may return to choreography on more than an occasional basis.
The combination of SAB and the NYCI seem to have nurtured a lot of choreographic interest at NYCB. Current and former dancers who have had ballets danced by NYCB include Albert Evans, Damian Woetzel, Edwaard Liang, Melissa Barak, Benjamin Millepied and Christopher Wheeldon. Several other dancers have taken part in a NYCI session. Not that all of them a brilliant choreographers, but I believe that the more people who are given the chance to choreographic, the more likely the real talents are to be found.