When user click on "Switch user" button, he is presented by "Select a user" interface, followed by login screen but he is again prompted for Username, disregarding that user already made choice.

So, either choice at first instance should be passed on, either as pasted username waiting for just one click and then password or simply password, or user should be brought by login screen instantly after clicking on Switch user button, thus overriding "Select a user" intermediate.