It would seem that recumbent bikes would be the ideal solution for randonneuring. And in the last dozen years or so, I can think of 11 recumbent riders in the local randonneuring club, plus one or two I'm overlooking no doubt. Exactly zero of them are still doing randonneur rides on a regular basis. One of them might sometimes, but he's just as likely to be on road bike or velomobile. I think four of them are currently riding upright bikes rather than recumbents (more gravel/mountain than road bikes).