This is taught in the intro class in basic numerics. Methods are considered more robust and practical if they have larger stability regions. Von-Neumann is the OG analyst for PDEs

> Those kinds of models aren’t really realistic? Energy goes to infinity, angular momentum goes to infinity, the chemical concentration goes to infinity: whatever you’re modeling just goes crazy! If you’re in this scenario, then your model is probably wrong. Or if the model isn’t wrong, the numerical methods aren’t very good anyways.

Uh... that's not how it works. The whole point of making a model and using a simulator is you don't already know what's going to happen. If your system is going to blow up, your model needs to tell you that. If it does, that's good, because it caught your mistake. And if it doesn't, it's obviously wrong, possibly in a deadly way.