By filtering to search, which is also a UI fraught with inaccesiblity if not very carefully designed. I think custom elements aren't the issue here really, it's the lazy implementations.
Think bigger even. In an ideal world, if you have that many options you might want to rethink the entire workflow. I understand in the real world that may not be an option, but it’s still probably the ideal state.
The only way to make a 200 item select box usable is to make it not a 200 item select box somehow.