So like, if you had a companion with you when you interacted with the fallen satellite at the Mohave Drive In, what reason can you think of why they wouldn't have been dragged along with you to get brain-scooped and go through a buncha wacky misadventures in the name of science?

New Vegas kinda just auto-fires vanilla companions with no explanation or reaction.

Well with the first two DLC's, you had temporary companions in them, so obviously they wouldn't want you to have your own companion. Also, the DLC's tend to be more story driven, centering on the player's character. Lastly, if you want a "game answer", the teleporter may have only been able to take the player to Old World Blues because of the different "brain grooves" as a result from being shot in the head. Thats how you're different than all the other Lobotimites. Hope this helps satisfy your questions

Yeah, I agree that a companion wouldn't fit in the first three DLCs so far and that a companion would've been turned into a drooling Lobotomite if they had indeed come along due to their lack of the special brain grooves, but that the player character turned out to be okay was a bit of an anomoly/surprise for the Think Tank and Mobius deduced that it was probably because of the bullet hole. So they wouldn't have been searching for this brain groove anyway

I'm probably just too nitpicky. The whole DLC was a bit off, imo. None of it really felt like it fit with what I understand about the Fallout universe. Trying to logically explain my companion's absense from Big MT when there really is no explanation.
Just the way it was.

Companions would've had limited survivability against the unstoppable death machine that is Big Mt on hardcoe, and would've given you too much of a combat advantage on regular.

Not looking for a game-design reason
I mean storywise.
Why would the companion have been overlooked by the Think Tank when they were bringing the Courier over to Big MT to scoop out his/her brain?
Wouldn't they rather have had two brains to scoop out?

They weren't dumb/curious enough to touch the satellite? On that note, it would be nice if they were surprised as hell when you come back alive from Dead Money or Old World Blues and acted like they thought they were never going to see you again.