Yes, I would have to detach the browser window, move it to the other screen (which is inconvenient because it has to go through a third screen), drop it, fullscreen it, press play, and when it's done close the window.

Much more involved than a single click that never even has to open a new tab.

Depends what's being watched, but quite often with content like How-To's, conference talks, and lectures etc I take advantage of having speed control on a keypress ('[' or ']' = +/- 10%), left arrow to skip back a few seconds, backspace to drop to normal speed if I miss something, 's' for screenshot of an interesting graph or chart etc... At other times I might make more use of ',' and '.' to step back and forth one frame at a time or '4' to increase the brightness.

Using key presses to navigate through and control media like this feels vaguely reminiscent of the first few times you really grok the power of editing a huge file with some well articulated vim or emacs commands. Also mpv seems less resource intensive whilst the browser has a lot of tabs open.

Videos are horribly choppy when I try to view them fullscreen in a browser. It's like playing a game without V-sync on. The same videos work flawlessly in MPV. Firefox in Ubuntu 18.04 with a Nvidia 750ti and proprietary drivers. YMMV.