Staff would have to answer but I'm pretty sure it is influenced by demand of a variant and how popular they feel the variant would be.
Variants in chess.com Live
Okay, I figured that would be the case... do you know if they respond to these posts, or is there a better way to reach them directly?

Your best bet would be to open a Suggestion ticket, though you could also create a topic in the Site Feedback & Suggestions forum, to see if others would be interested.
https://support.chess.com/customer/portal/emails/new
Hi, does anyone know how the developers of chess.com decided which variants were available in Chess Live? Is it by popular demand? I have a variant suggestion for a Chess Live variant that would not require too much development (trying to get my idea out there, aside from the Chess Variants website).