Every akhal teke owner in the world should read this! Just replace the word Arabian with Teke, and it will be perfect. I've always believed that our breed should have a greater percentage of evaluation during grading that is geared more towards accomplishments instead of beauty contests - especially when it comes to breeding.
My own horses do both show and endurance. There is no harm in having multiple careers with your horses, in fact, it's somewhat of a "fail safe" plan. If one path doesn't work out, you can always go with the other path. Patti is a great ambassador for this kind of multi-tasking. If the rider keeps an open mind, they can be both proficient and successful doing different careers with their horses.