When Player 1 (Human) is not in the game, (or leaves partway through) I have a trigger that creates two missile turrets in predefined locations for Player 1.

When I try to remove these turrets, the game decides that it doesn't want to.

I have tried these actions, the trigger executes but the turrets remain:
- Remove all turrets owned by all players.
- Remove all turrets owned by all players at anywhere.
- Kill all turrets for all players

The trigger is run by Player 4 (a CPU).

Okay.

- Remove all turrets owned by Player 1.

Works. StarCraft can be lame like that.

(Close me.)

Yes, ghost players (and the units created for them) are not counting towards All Players. However units of leavers go to P12 which IS counting towards All Players.
Best fix: Avoid creating units for ghost players by always using Current Player when creating units. Generally you should never use specific player numbers if it's not a computer, or if that computer may be defeated.