This episode does have a few things in it that make it less awful than Plato or And the Children Shall Lead:
1) I believe this is one of the first mentions of ion power in a popular sci-fi setting
2) An interesting free exchange among most of the bridge crew when deciding which planet to beam down to, more reminiscent of one of Picards endless staff meetings than the usual Kirk deciding everything.
3) When they beam down Kirks first order is to "set suit temperature to 72" and all the crew reach around to adjust some hidden control and then all the actors stop shivering. This is the only episode that provides any reason for why Starfleet landing parties never beam down with so much as a jacket or box of matches. They don't have to. Disparage Brain all you want, no other episode until the animated series touches on this.
4) Describing women as givers of "pain and delight" and the nodding assent of all the male actors is funny and an accurate description of them whether its the 1960s or 23rd century.
5) There is a bit of Kirk-Fu fighting when they try to get their communicators back, that's always welcome. Interestingly James Blish's adaption of Brain describes a bit of the "scientific style" of fighting that Kirk uses, in the screenplay this is only hinted at with Kirks line to Mccoy that "science holds the key to getting their property back".
The worst part of the episode is Nimoys obvious distaste for it. As an actor all he could do was maybe put some varied inflection in his voiceover scenes as the Controller. Otherwise he was a robot for the full hour and you could see the boredom.
Is it lazy writing that the Great Teacher has all the needed skills to put the brain back? Sure, but its in great company along with the Fabrini having just the cure for Mccoy, the Mugato root for Kirk, Pulaski's hair brush DNA sample, or Crusher being able to reverse DNA changes in evolution in the time it takes Picard to record a log entry.