Richard Hamming has a story where he was shocked/appalled that some folks wanted to include him on a paper after he suggested using Linear Regression in an obvious application of linear regression. The upshot is, if it were obvious it would have been done already. So many times people have done everything they can to avoid using a matrix decomposition or a proper filter.

I mean yes and no? Kalman filters fuses information about known system behaviour along with observations in an optimal predictor (for certain types of noise). It uses a matrix in the same way that almost every operation on a computer uses a matrix.

Edit: I missed the quip about the Kalman comment being in jest, my reply probably wasn’t necessary but I’ll leave it up.

In my area, every controls engineer says "we can just use a PID".

99% of the time it seems they're not wrong, despite control engineering being a pretty large area of research.