Rockstar has made the disabling of saves once a cheat has been activated something of a rule in their games.
This, coupled with the disabling of achievements too, further support the idea that perhaps cheats in Rockstar titles aren't "cheats" in the traditional sense, but optional gameplay modifiers designed to simply be fun to play around with once you've exhausted the regular content.
Deactivating achievements makes sense too - they wouldn't be worth much if anyone can cheat their way to unlocking them.