Frankly, if you must hamper the ENT-A's functionality (Which seems necessary for the story) Then instead of the lame "No experienced commanders" excuse, you could just say the whale probe somehow damaged all their vessels in the vicinity, as it passed through to Earth, & that because the A wasn't in service or finished yet, it had no such difficulty. That probe did after all paralyze everything it came near, & that phenomenon's extent is largely unknown.
It would also help explain away why the new Enterprise was so hastily patched together. Besides wanting to reward Kirk & crew, they needed to get a ship out there on duty, while everybody else was scrambling to get fully operational again, after the events of the last film