> They really should try to come up with algorithms that are more intuitively linked to a spatial comprehension of the numbers.

Have you heard of "chunking"?

This video shows old style long division (and you're right, the method is confusing). It also shows an easier method that is based on understanding numbers rather than just applying an algorithm by rote. https://www.youtube.com/watch?v=K2rBaSj2L74

Here's another explanation: https://www.theschoolrun.com/what-is-chunking