First, Plack time and Plack length are not minimum units. There are thing smallers/shorter than that. They are in no way special limits. We have so far not discovered lowest instant.
Things in low scales are not random because of inacurracies, but because they start to be more like fields - fields that actually have "peak" location. If somehowe it was caused by underflows, we would see very clear patterns and aliases.
In any case, it is very trivial to simulate sub-frame things in our computer simulations.
Seccond, you can not measure speed and position at same time not because of some weird universe limit, but because you effect particles by measuring them - usually in unforeseen ways. There is no hint of optimalization.
Third, collapses do not work like that. From point of view of universe, everything is observed eventually and anyway. And actually computing whether something will be observed sounds like too much work to be considered a optimalization.
Simply put, pop sience descriptions of our understanding of universe are doing you disservice.