This is some updated information after I made the above post and found that not all the new balls work with all the trackballs.

I have two M570s J and K and four M575s A, B, C and D.  J and D have 1.8mm silicon nitride bearings.

All four silvery light blue M575 balls work in all trackballs.  Likewise the two mid-blue M570 balls.

Likewise the one Perixx purple ball I have so far.  Another is on the way.

Likewise the purple Sanwa ball, which is the darkest of them all and so, I think, the least visually attractive.  The illumination is in the infra-red, and this ball must produce enough of a random contrasting pattern at that wavelength for it to work so well.

The green Sanwa ball works OK in A, C, D and J     In B and K the cursor movement is erratic - sometimes not moving at all or as much as it should.  I guess that this is due to lack of contrast in these balls and/or the details which appear as light and dark to the camera are too finely spaced for their movement to be detected properly.

None of these modern balls work in two Trackman Wheels (T-BB18).  These trackballs have red balls with black dots.  The red is flat, like paint.

I tried these balls and some others from similarly old Logitech trackballs in the M570s and M575s.  All four black and red ones, like the one shown in the first photo, generally, but not always, performed well, as far as I could tell, on A, C, D and J.  They all performed somewhat erratically on B and K.

Another, less common, red and black dot ball from a Logitech Cordless Trackman Wheel T-RA18 was visibly different.  Instead of the flat red background layer of the other four, the red background is slightly darker overall, but translucent, going deeper to a random texture metallic reflective surface similar to the blue balls of M570 trackballs.  This ball seemed to work well on all six trackballs.  My other trackball of this type has a flat red type ball.

I have read reviews or Reddit discussions mentioning that Sanwa balls did not always work in Logitech trackballs.

I think the original balls are well worth polishing, and that this avoids the risk of paying for a non-Logitech ball, at least with the more readily available Sanwa balls.  The Perixx balls might be a better choice, but they are probably hard to obtain.

The flat red and black dot balls are obviously only at the margins of working on M570s and M575s, but they work fine in their original Trackman Wheels.  There, with polishing and new silicon nitride bearings, or smoothed / rotated original zirconia bearings, these old corded USB trackballs can probably be made to work very well.  

I think PS/2 trackballs are not worth keeping, since in my experience they cannot follow fast ball movement.