I find Green's role in that archetype is very different than Red's. Red holds most of the archetype "payoffs", but green has two of the best enablers in
Wild Mongrel and
Noose Constrictor. Green is also great at mitigating the impact of discarding cards that aren't themselves madness payoffs. What I mean is, say you have
Bloodrage Brawler in your opening hand. You want to play it turn 2 for maximum effect, but you want to save discarding, say
Fiery Temper for a time when you can pay the madness cost and get good value.
Green says "no problem!", discard a land for the Brawler and we won't lose any value because we'll play it with
Ramunap Excavator later on. Or, discard whatever you like and we'll get it back with
Regrowth or
Eternal Witness. I feel like these Madness decks want to be enabling their discard engines as much as possible, which often means activating them when you don't have a literal madness spell to cash in, and that's where Green shines. It's general recursion adds consistency alongside Red's potential for explosiveness.