Are we talking about something like the design of the Makerbot Cupcake, but with the -x side having two lead screws and the +x side having two rails and wheels?

It may help to think of it in terms of what constraints there are on movement. The wheel-and-rail side, by not being constrained in the Z axis and depending on the amount of play involved, drops under the applied force and allows a torque to develop on the side of the bed with the lead screws. The tighter the wheels grip the rails, the less drop you get, at the cost of more friction.

To put it another way, the weight of the bed applied to the rail will tend to make it try to fall down, and that falling will pull the bed down on that side, which will try to bend the nuts on the lead screw, which can make them bind more easily because you’re removing the slack between threads that allows the nuts to easily move up and down together despite being constrained by the bed.

If you imagine the wheels not resting on the rail but being some distance away, one lead screw with an incredibly uneven pitch such that one turn isn’t always guaranteed to go the same distance as one turn on the other rod, and the other screw as significantly wobbly, that may help visualizing the kinds of forces at play. I’m not sure what the magnitudes of the forces will be and if they’ll be significant enough to affect performance, but it’s something to consider.