It obviously wasn't designed as a deep space explorer vessel
Please explain how this is obvious. For one, I'm not sure the term "starship" would have been likely to mean otherwise to the production team at the time she was conceived, but I also don't see any particular reason why she can't carry out such a mission.
It's certainly not because of the size difference. She's a little bigger than the TOS Enterprise
and only 8% smaller than the movie version.