I cannot overemphasize the extent to which I am just some guy

There's a weird clause in the family will that says he has to have a kid by the time he's 30 (or 40) or he's unable to inherit. Think of the movie Seven Chances (1925), or the remake The Bachelor (1999) (don't... don't watch this movie), only it's about kids and not marriage. Losing the money isn't a big deal to Carter tbh, but the rest of his family hate Carter's dad so much they're like 'please he sucks, we don't want to have to kiss up to him, and he keeps losing money on the stock market. Think of the good you could do or whatever. The good for us.' Part of him does want to get back at his dad, but the actual good he could do with the money seals it. Insert newly awakened breeding kink thoughts here ;)

He knows his kidneys are going to fail in the next few years. Anti organ rejection meds and pregnancy are incompatible, so if he wants to have a baby he has to do it NOW. Who wants to be pregnant on dialysis? Benton and Luka have had kids before, so if he asks one of them to donate, he doesn't have to worry about fertility issues. (He doesn't know Reese isn't biologically Benton's and Benton isn't going to correct him). Cue a comical misunderstanding where they both try and fuck him pregnant. Like hell is Carter going to correct them.

Carter and Benton are together. Benton doesn't want another kid because he wants to focus all his love and attention on Reese. What's that? Reese wants a sibling?