You can have very complex calculations and a simple output. The complexity of the process to find the weights is not necessarily the same complexity than the process using them. The numbers don't get suddenly special because of how they were calculated (like 42 is just the number 42 even after 7 million years of calculations).

The difference is the capabilities. LLMs don't necessarily need billions of Parameters. In fact, useful models (like the one used in never Apple devices' autocomplete) has only like 50 million. Markov chain... I guess there is probably a reason why we don't use them instead of neuronal networks. Maybe somebody more knowledgeable can enlighten us, but I suspect one might need magnitudes more parameters.