Nonsense.
We could easily go through an A-Z of races and cultures discovered during TOS!
The primary exploration ship during the time of Star Trek: TOS was the Constitution-class cruiser of which the USS Enterprise was the most famous ship of that line. There were 12 such ships engaged in the second exploratory phase of the Federation as it began to expand and meet other alien species. This expansion would eventually be limited by the Romulan Neutral Zone and the border to Klingon Space.
Let's look at the first five episodes of each season of TOS:
The Man Trap is about the Enterprise checking up on someone else doing the exploring.
Charlie X features the Enterprise transporting a passenger.
Where No Man Has Gone Before is about exploring
The Naked Time the Enterprise is responding to a distress call and investigating mysterious deaths.
The Enemy Within does feature exploration
Amok Time is about getting Spock home to Vulcan for his wedding (so to speak).
Who Mourns For Adonais is about the Enterprise being pulled away from its duty by an alien douche posing as a god.
The Changeling they are defending themselves from a probe bent on destruction.
Mirror, Mirror starts with the Enterprise negotiating for Dilithium crystals before the plot about the MU begins
The Apple is about exploring
Spock's Brain they are attacked by aliens and follow them to their planet to retrieve Spock's brain.
The Enterprise Incident is a military mission. No other way to look at that.
The Paradise Syndrome is about exploration.
And the Children Shall Lead is answering a distress call.
Is there in Truth no Beauty is about the Enterprise transporting an alien dignitary.
So out of those fifteen episodes only four are actually about exploration, with one more related to exploration. I can go through every TOS episode if need be to back up my claim.