I'm not particularly fond of the button myself but I admit I had never really noted the reappearance before.

(In reply to comment #0)

Please, instead, have it just appear when the text field is focused and stay
there until it is unfocused.

Note that this proposed solution doesn't fit all text fields, for instance search bar and even edit summary often depend on its disappearance to show suggestions, and in general it's not a safe assumption that the tiny space in the corner is free for permanent use.

The menu was designed to work for any input field and text area. Input elements are used in many different contexts and we cannot force extension developers to leave space to make the IME fit nicely in a specific fixed position. As commented by Nemo, that could break things such as search suggestions by making some UI elements hidden by the menu.

The idea is that while the user is focused on inputing text we provide the menu, but when the user is focused on another interaction (that the menu may be blocking we make the menu disappear). We provided a delay that we thought it was good enough for regular typing speed and we created a smooth transition that makes the menu disappear into the text area to communicate the user that he can bring the menu back from there. CSS transitions were used to make the transition smooth and avoid distracting the user.

Users that need to often switch between input language will probably find the menu useful. But we also provided a way to remove it for those users that don't need such support. By going to "More settings" and selecting "Disable input method tools" you can avoid the manu from appearing at any input box.

Closing this as WONTFIX per comment 2. We cannot disable the IME by default, because that reduces discoverability to almost 0. We also need to blend out the keyboard icon to that it doesn't continuously block the UI.

Comment 2 describes a method to fully disable the icon from appearing if you never need it.