Very sensible thinking!
My expectations come from experiencing building, re-designing, and designing 3D printers. There, you will find very obvious artifacts in the print if you try to use a lead screw as a combined lead screw and linear constraint. I don’t know that I actually need to do any of this, but I’ll describe how I got here.
Initially, the rods were entirely necessary for alignment when it was suspended from UHMWPE line. So the question was whether to remove them from the design when moving to lead screws. I’m not sure whether I would have added them in the first place if I had not been trying to suspend the bed in the first place.
Lead screws are made of 300-series stainless steel; linear rod is hardened steel, so lead screws are more flexible than linear rod even before accounting for the smaller effective diameter of the internal thread diameter. The lead screw nuts are a loose tolerance fit; if you thread a loose nut onto a piece of lead screw you can feel the loose tolerance in slight wobble. Finally, the screw is not necessarily as straight as the rod in the first place.
Straightness doesn’t matter if you only use the Z axis to get a flat part into focus and are never driving it while lasering, and if you are never putting a lateral load on the bed, the flexibility and loose tolerance probably also is no problem. So for typical use, this is probably fine.
However, I can think of two reasons; one practical and one theoretical, to keep the linear rods. The possibly practical consideration is that this has a 1500mm X gantry, which means that it has substantial mass to shift in the Y direction. The frame is lighter than a typical steel laser box, and the larger the ratio of gantry mass to machine mass, the more the whole machine will react when the gantry moves. I would expect that shifting from engaging the front lands to the back lands in the nut would be enough shift to create visible artifacts on parts. The entirely theoretical consideration is that in one imagined use, I might first use the OX to route out a relief, and then engrave on that surface with variable height and want Z to track to keep in focus. I have no plans to do this, but the idea of someday being able to do that and keep good alignment throughout is intriguing. It’s not likely that I’ll ever do this, but it’s nice to think that I haven’t closed the door on the idea.
If I have any problem with binding, I have an alignment problem. The question then is whether I have the skills and tools to resolve the binding problem. Since the screws rotated reasonably freely when the bed was aligned well, I think I’ll be OK here. One I have a belt in place, I plan to loosen the upper attachments for the rods and the rear two screws, run the frame as high as it can go, and then tighten the upper attachments. (I already aligned at the bottom.) If the screws still bind, I can loosen one of the front screw attachments as well to fix side-to-side alignment.
I could reasonably go with one linear bearing on either side. So if I have problems with binding I could take off a pair at opposite corners and simplify. But this huge bed frame (850x1500) isn’t really stiff, so I’ve been taking the approach of considering each corner somewhat independent. Logically, I should be lifting at three points not four, since three points determine a plane. If the bed were stiff, I would probably do that. But it’s not stiff enough for that; I’ve measured I think approximately 5mm of “potato chip” deviation from flatness earlier.