You use your Web browser to go to a web page and there's a video. How do you play it? Your browser uses some sort of plugin. This is not an example of the "Inner Platform Effect" but simply the most efficient and straight forward way to do it.
I am perfectly aware that for some people (most people?) playing the video embedded in the browser might be the most straightforward way of playing it. For some it might be somewhat challenging finding the "save as" option in the context menu, and deciding a path that later they have to find again, but...
Embedded video players are the worst video player ever. Ever. There, I said it.
I'm following a class in Coursera, and the first thing I do is save the videos as local files and play them with VLC. When I press the spacebar to jot down something, sometimes the video pauses, sometimes an invisible blank character is written in a text field of the page, or some link that has the focus is accidentally clicked.
If the embedded player in the browser can't get right something as simple as toggling the playback, don't get me started on the convenient shortcuts that a video player has to play faster and slower, or going some seconds/minutes/hours forward and backward.
Browsers are nice, and some cool fancy webpages can be done combinating transitions, text, images, and yes, video, but attempting that a browser is going to be a good video player is never going to happen.