Well a belt placer is just fine and can easily handle 0201, but you have to enter a little bit control theory.
Linear encoders aren't that expensive, stick them onto the gantry and take the position from that. You can even get a nice index from them they will make the accuracy pretty good.
Even ASM is using belts in some pick and place machines.
My background is CNC machining, and pick and place machines are just a subset of that.
I have my own software so I can only complain about myself if something is not implemented.
I don't think any current ASM machine is using belts, and take a look at the belts used on something like a D2 launched like 15 years ago
https://www.youtube.com/watch?v=miy3HxlcwUg. Its on one axis and its a chonker. The other axis looks to be linear, the new machines are all linear. Our Essemtec uses belts and is rated for similar placement accuracy, they are also chonky and yes they are backed up by encoders. Essemtec wants users to replace them every 2 years, the new models.. linear. I'd say ASM was an outlier in belt usage then, even ball screw seems retro now for full size machines.
Even allowing for the much lighter gantries and heads on desktop p&p the belts seem way too puny to be trusted to stay in spec, even so its feeding that will probably let you down. 0201 in paper tape will be much more forgiving than plastic tape, and 0201 size diodes for instance can be in very shallow pockets needing very smooth feeders.
Tiny volumes, Tiny budget, no
real need - won't miss that $1800 too much, maybe try the Lumen it looks like less work than a liteplacer, and the other is a total unknown. However flawed I might consider the approach, it has grabbed some community interest which can only help and at least they are looking at feeders and improvements.