All input elements with some concept of a picker have a showPicker function that opens that UI. Adding this to <select> was marked as future work in whatwg/html#7319. However, a subsequent request for this behaviour was raised in whatwg/html#7957.

It would seem like a relatively simple addition to <selectlist> and I imagine there's more use cases for it like the above issue.

It's worth noting that while showPicker() doesn't exist for <select>s it does work for inputs with a datalist attached (inside of Chrome other browser may vary).