More importantly, this is not as powerful as true multiple dispatch like in CLOS. There is no way to call other methods, there is no way to specialize partially (e.g. combine the variant with subtypes, and define methods only for some combinations of subtypes and super types on the parameters, and allow the implementation to choose the most specific one).
Edit: to add a few more details on my second point. CLOS (and I assume Julia too) allows you to call 'parent' implementations from a child implementation, similar to calling base type methods in virtual dispatch - you can call the next-most-specific method that would have matched the params, which you can't with the visitor. Also, say I have a generic function F(Foo, Bar). I could define methods for F(FooSubtype1, Bar) and F(Foo, BarSubtype1), and then call F(FooSubtype1() , BarSubtypeOfSubtype1() ) and have the right implementation get called (F(Foo, BarSubtype1)).
It's far from the same thing though, less convenient and less flexible.
Multiple dispatch doesn't require a centralized declaration of the possible types and allows putting implementations in different files.
we're in 2020
works fine (and has worked fine since a long time with either boost.variant or in C++11 with eggs.variant, etc...)