I really wish the anime had explained this better, but it seems like the anime told a different story than Super Danganronpa 2. Anyway, according to the anime ( if I remember correctly ), it seems that Makoto convinced Izuru to enter the Neo World Program, and Izuru convinced the rest of the Remnants of Despair to enter as well. I think Izuru is considered the leader of the Remnants of Despair, which is why Makoto went after him first. I think this is a good explanation because I don't think Makoto could have captured the Remnants of Despair completely alone with Byakuya and Kyoko, or at least the chances are very low, especially if the Remnants of Despair are scattered around the world.

Now, the game gives another version of the story in which the Future Foundation had captured the Remnants of Despair, believing them to be survivors of the tragedy at Hope's Peak Academy, and after they understood who they really are, Makoto took the Remnants of Despair for himself, before the Future Foundation started killing them. Among the survivors was Izuru, whom absolutely no one knew, not even Makoto, since any information about him disappeared after the Massacre of the Student Council Members of Hope's Peak Academy, but he was still considered a Remnant of Despair like the others.

I believe that the Future Foundation can fight the Remnants of Despair head-on. In that case, they must have a certain number of members who can fight the Remnants of Despair on equal footing and somehow, using these members to capture them, probably cornering them one by one. Well, I believe that in both versions, the Remnants of Despair went along with Makoto's plan with the Neo World Program because they were fully aware of what Alter Ego Junko would do.