There will be no need for a dedicated training carrier, the smaller air wings on fewer ships don’t need as many hours for carrier-qualification/requalification as before, especially with modern simulators for much of such training.

For a long time the USN has used whatever carriers are in post-overhaul workup (or recently returned from deployment) status afor training duties… remember that JFK did a Med cruise in 2002, and was in the Arabian Gulf in 1997, 1999, & 2004… there was no dedicated training carrier then.

Besides, the JFK hasn’t operated aircraft for several months, since she was de-certified for flight ops (arresting gear found to be unsafe before Feb. 20, 2006).

Note the comments & ship’s history here:
http://navysite.de/cvn/cv67.htm