It really doesn't.
Languages like PHP and Ruby "have won out" over statically typed languages because the representatives of statically typed languages at the time were Java and C++, both of which were bad (they still are, but they were): verbose, difficult (and verbose) to leverage for type-safety, missing a bunch of tremendously useful pieces (type-safe enums to say nothing of full-blown sum types), nulls galore, …
As a result, the gain in expressiveness and terseness (even without trying to code-golf) of dynamically typed languages was huge, the loss in type-safety was very limited given the choice was "avoid leveraging the type system" or "write reams of code because the language is shit", and the fast increase in compute performances more than compensated for the language's loss in efficiency.
And that's before talking about the horror show that Java's web frameworks ecosystem was circa 2006.
> Languages that tend to work well with it are those that are highly flexible around the corner cases of these technologies, and allow you to quickly iterate through the process of gluing them together.
That's really complete hogwash outside of the client, which isn't what we're talking about here since neither php nor ruby run there. On the server you have clear interfaces between "inside" and "outside", and there's no inflexibility to properly taking care of cleaning up your crap at the edges. Quite the opposite, really.
