You are right that integer linear programming is NP-hard; but faster algorithms for continuous linear programming are also super interesting and impactful.

Continuous linear programming is also _hard_. Not in the sense of NP-hard, but in the sense of there being lots of algorithmic and engineering aspects that go into an efficient, modern LP solver. Even just the numerics are complicated enough.

(And many integer linear programming solvers are based on continuous linear programming solvers.)