Understanding classical waves better is what helped me wrap my mind around the physical meaning of the uncertainty principle. It's not a technical limitation, and it's not just because you need to interact with something to measure it. It's just a property of waves. Since small enough particles exhibit the properties of waves, it only makes sense that we can't know their location and momentum at the same time with arbitrary precision.

The velocity of a wave is a function of its frequency and wavelength. But imagine a highly localized wave, essentially just a peak. What's its frequency? Well, we find that it doesn't have one frequency! If you decompose the wave, you find its mathematically a superposition of multiple sine or cosine functions with different frequencies and therefore velocities. So the more localized the wave is, i.e the more you know its position, the less and less you know about its frequency and therefore velocity.

This stuff blew my mind when it was first explained to me.