Agreed. I am a huge believer that you can get to answers quickly with a Monte-Carlo analysis. But I'd take it a step further and include how to solve differential equations numerically as well. You'd be amazed at how far you can get with Crank-Nichols, Lax-Friderichs, and even simple central differences methods.

Additionally a lot of stuff people use in machine learning today had its start in solving physics or communications problems numerically. Stuff like maximum likelihood detection, gradient descent, etc...

I also believe that implementing code to solve physical problems really can deepen ones understanding of physics. Once you have something you can really play with it and see where things break etc...