What is the relevance of Fresca in the show "The Boys"?

Unfortunately, none

It's an in-house joke by the writers..

A simpler explanation of the abundance of Fresca has recently been offered by showrunner Eric Kripke, and it's not as exciting as fans once hoped. Kripke confirmed that the Fresca bit was a running gag in the writer's room that made its way into the finished scripts, stemming from a discussion over what Eagle would offer The Deep as a non-alcoholic beverage. This is due to the fact that many religious organizations dissuade their members from consuming alcohol, or engaging in excess with controlled substances.

and

Then Fresca just came from...honestly, I wish there was a deeper thought than it just became this running joke. We were laughing because we were thinking about like, 'Okay, what does Eagle the Archer serve him to drink? Was it alcohol? No, no, he's in this cult, and they don't drink alcohol. What do they drink?' And I don't know who said it, but someone was like, 'Fresca! They drink Fresca!' And we just started laughing, because for some reason, it seems like the drink of cult members, which I think is going to be their new advertising slogan next year: The Drink of Cult Members. It just seemed like something they drink, and so we just started putting it in more and more. You'll see once you see the whole season, we keep that joke rolling all season long. [Laughs.] That Fresca joke does not stop. It is right up until the very, very end of the show, we had Church of the Collective members drinking Fresca.

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