Worked in the securities division of a leading investment bank for 8 years including on the equities exotics and hybrids trading desk. And I can confirm that we used to use MC whenever we had something we couldn't price using a closed form method. That said, it's a lot slower and more compute intensive so when you could use a grid pricer or pde solver or whatever people would use that instead.

You're not really simulating every outcome, just a "large enough" representative sample.

As an aside, my dad was a chemical engineer and Newton-Raphson was his equivalent everything-is-a-nail numerical method. We used to use brent root and monte carlo simulation in the same way.

Numerical methods are awesome in general.