For example, it is helpful to avoid having to do tons of explicit integer parsing when working with the DOM, which uses strings for everything

Yes. You have a list of floats and you want to add n to the n-th element. Then n is both an integer (when indexing the list) and a float (when adding).

Of course the language can require an explicit cast, but in most cases it goes against the intuitiveness and simplicity that dynamic languages want to achieve.