Rapidly switching on and off a 12v power supply, bad idea?
Probably the fuse will die in short order. Everything else will probably be okay, but it's additional stress that will tend to shorten the life of the rectifiers and main filter capacitors in particular. Schurter says: 


  Inrush Current Peak
  
  Continuous exposure to pulses of high current could prematurely age the fuse.
  The number of pulses the fuse would be exposed to in the application should also be considered when choosing a fuse. 




If the PSU uses a circuit breaker rather than a fuse and your switching frequency is low enough that the breaker has a chance to cool, it may be okay, at least in the short term. 10 minutes 'off time' is long enough that any inrush protection thermistors should have a chance to reasonably cool down. 

Very short off times (seconds) could be close to worst-case and may damage parts other than the fuse relatively fast, as well as causing thermal cycling.