What are the typical problems in physics that can be solved by momentum and impulse?

In some cases where kinetic energy is not conserved, momentum can be conserved, such as the case where friction does work. Momentum conservation and energy conservation are two independent laws, and universities will also learn angular momentum conservation. All mechanical problems are solved through these three conservation. So it must be good to master one more.

Complaining about deleting motivation is definitely a failure of high school education. Newtonian mechanics without momentum.