We used to do this sort of mix & match as kids screwin' around the neighborhood. I even had a tiny scooter wheel on my BMX bike for awhile.
As for usefulness? I don't think there is really much benefit to doing so randomly. But practicality aside, & assuming disc brakes, there are cases where it could theoretically make sense. One example would be installing a suspension fork on a 29'er/700c rigid. 54x559 is really close to 700x23c. In theory you could swap in a suspension fork & 26x2.1 tire & not terribly disturb headtube angle/rake too terribly...not that it would make sense for most bikes though--The rear wheel would need frame clearance. I wouldn't take such a bike over more than a generically rough road with potholes, though.
Usually people just keep their rigid as a rigid & go with 27.5/650b for the additional tire volume.
Last edited by base2; 01-09-21 at 10:17 PM.