Justification for the Hungarian method (Kuhn-Munkres)
(Moved from a comment.)

Of course you can solve any LP by using a general-purpose LP solver, but specialised algorithms typically have a much better performance.

It is not only about theoretical asymptotic performance guarantees, it is also about practical real-world performance. Algorithms such as the Hungarian method can be extremely streamlined and they are relatively easy to implement correctly and efficiently.

You can also often avoid issues like using exact rational numbers vs. floating point numbers; everything can be done easily with integers.