> Things seem to be quantised at a low enough level.
Some things. But others are very much not: in particular, space and time are not quantized, and in fact are not even quantizable. A theory in which there is some discrete minimal unit of space (or of spacetime) is trivially incompatible with special relativity, so it is incompatible with quantum mechanics (QFT, specifically).
This is easy to see from the nature of the Lorenz transformation: if two objects are at a distance D = n*min for some observer, they will be at a distance D' = n*min*gamma for some other observer, where gamma is always < 1 for an o server moving at a higher speed in a direction aligned with the two objects. So the distance for that second observer will be a non-integer multiple of the minimum distance, so your theory is no longer quantized.
We do not know if spacetime is quantized or not, and there are theories claiming that it is (LQG etc). And sure, we don't have a coherent "theory of everything" that includes quantized spacetime, and the models that we do have are contradictory if spacetime is quantized. But we already know that those models are deficient.
Our current theories only work if spacetime is not quantized. Any theory that tries to quantize spacetime needs to somehow replace special relativity and its Lorrentz transform with something completely different, while still remaining consistent with the huge number of observations that confirm SR works - especially the extremely precise experiments that confirmed QFT. This is one of the reasons why LQG is almost certainly wrong, by the way.
Note that this is separate from the problem with GR-QFT inconsistencies. All of our current theories are based on and only work if spacetime is continuous. While it's not impossible that a new theory with quantized spacetime could exist and work, it's not at all required.
The one thing about spacetime that we do believe might be quantizable, and would have to be quantized for GR and QFT to be compatible, is the curvature of spacetime. But even if spacetime can only be curved in discrete quanta, that would not mean that position would be quantized.
Some things. But others are very much not: in particular, space and time are not quantized, and in fact are not even quantizable. A theory in which there is some discrete minimal unit of space (or of spacetime) is trivially incompatible with special relativity, so it is incompatible with quantum mechanics (QFT, specifically).
This is easy to see from the nature of the Lorenz transformation: if two objects are at a distance D = n*min for some observer, they will be at a distance D' = n*min*gamma for some other observer, where gamma is always < 1 for an o server moving at a higher speed in a direction aligned with the two objects. So the distance for that second observer will be a non-integer multiple of the minimum distance, so your theory is no longer quantized.