*Very* surprised this question has not been asked yet.

In almost every single episode, at least from the first season all the way through to the Unova region, Team Rocket is trying to catch Pikachu to give him to Giovanni. Why do they do this? They often cite reasoning that this Pikachu is special somehow, but is that actually true? Nobody else really talks about how awesome Pikachu is, and he certainly doesn't seem to win very often.

I'm looking for any kind of answer, in-universe, out-of-universe, thematic, humourous, etc.

I have a theory I will post below but wonder if this community could come up with a better answer.