I can only assume that there was some contractual obligation that Kirk appear shirtless in some specified minimum number of episodes per season, but this clause did not extend to McCoy or Spock. (Spock appeared shirtless in one episode - "Patterns of Force" - but that's all.)

And this is the episode where they clearly ran out of prop budget.

Transcript

1
Captain's log, Stardate 5121.5. Evacuating research station on Minara II, before the star goes nova.
Kirk: Where are they?
Caption: 4 shadows. Maybe 4 suns??
2
{inside the research station}
Spock: This record tape indicates the researchers vanished 3 months ago.
SFX: vanish! {McCoy vanishes}
Kirk: Bones!
Caption: They all vanish one by one!
3
{a dark place}
Kirk: Where are we?
Spock: Some sort of sound stage with minimal props, approximately 121.32 metres below the surface.
4
Spock: A humanoid female.
McCoy: Mute; no vocal cords. I'll call her Gem.
Kirk: The secret to this place must be in her mind. If only there was some way for one of us to... meld minds with her.
5
{Kirk is chained up, shirtless}
Thann: We are Vians. We will torture you in front of her for no readily apparent reason.
Kirk: With my shirt off, it won't be torture for her!
6
McCoy: Jim! Are you okay?!
Spock: Wait. She is an empath. She is healing him by transferring his wounds to herself.
7
Caption: In an over-emoting competition!
{Kirk and Gem emoting}
8
{more emoting}
9
Lal: Now we shall torture McCoy for no apparent reason.
Thann: And leave his shirt on for no apparent reason.
McCoy: Aaargh!
10
Thann: Now we see if Gem will sacrifice herself to heal him.
Lal: We can save just one civilisation from the nova, and want to see if hers is worthy.
11
Kirk: You're monsters! You have no compassion!
Thann: He has a point. Let's heal McCoy and save her race anyway.
Lal: Eh... Sure.
12
{Enterprise bridge}
McCoy: So... they just vanished, and we fly off without knowing what happened?
Kirk: All's well that ends well! Allons-y!