Hi!
Personally I dislike mod buttons cluttering up the screen. It is of course possible to add a setting where you can hide the button, but it's also annoying that you'll have to click through x mods to disable such buttons at the start of a new game. If I were to make it hidden by default then the user would have to know about the key binding, more or less making a button superfluous.
I won't change anything for 0.14, but I'll take it into consideration for 0.15, if this mod is still of any use then (seeing as they're promising a research overhaul in 0.15).
As for which mod wins when multiple mods share key binding, they all (should) win, i.e. all the mods get invoked. "Should" because there was an issue with this some versions ago, but it should be fixed now.