After a bit of searching I found a calculator
to get an indication of the degree of movement the sensor may need to be moved when close focusing.
The calculation is for a simple single lens element, so in practice retrofocus or telephoto designs would be a lot more complicated. Still, it gives an idea of the kind of distances we're looking at. In particular, the distance from lens to image at sensor (b). Focal lengths stated here are actual lens focal lengths.
First let's take the good old 50mm lens. Going from infinity to 1m, the calculator gives an increase in "b" of about 3mm. Not bad. What about 35mm? The calculator gives 1mm there, but we're running out of its displayed resolution and can't go any wider. It could be challenging to move quickly and accurately for wider angles. For comparison, the Canon 35mm f/2 lens extends by about 2 or 3mm for the same distance. I think it would be a mild retrofocus design so in general that might help out.
How about longer focal lengths? Again going from infinity to 1m, for 135mm we're already at 26mm of extension. At 200mm it's 76mm, which I think means we're out of room. Increasing the MFD to 2m brings it back to a manageable 25mm again. Obviously at longer focal lengths you'll need longer MFD to have enough room. Like existing macro photography, you could use extension rings to reduce the focal distance range.
One interesting point here is that as a fixed focus lens, you wont get the focal length shrinkage effects seen at close focus on many modern lenses.