Not just practically impossible, it is theoretically impossible. Given Heisenberg's uncertainty principle, observing a position with a certainty of the planck length would require it to have so much energy that it forms a black hole. Since you cannot get information out of a black hole, this makes observations below this scale impossible.

Of course, the scales involved are far beyond anything we have been able to probe. And this arguement relies fundamentally on the interaction between gravity and quantum mechanics, even though those theories are famously not compatable. So the 'theoretically' in theoretically impossible is doing a lot of work.