You don't need to call for a taxi from any of the WDW resorts. They are normally waiting outside all the resorts. If one is not there a Cast Member will get one for you right away.
I understand taxis are available outside the theme parks somewhere beyond where the resort buses load. This would not be true for the Magic Kingdom as only Disney buses are allowed near the main entrance. I read a post recently about taxis being available at the TTC, but am not sure where. It would still be easier to get one from any resort rather than go to the TTC for one. The TTC is rarely used by Disney resort guests anymore. It is basically the starting point for off-site guests to the MK.