Uploading large files to your own webspace is NOT a good idea.
That depends…I upload a lot of my training video that’s intended for general public viewing to YouTube and simply embed the video in my sites…like here:
https://educhalk.org/blog/
And as you point out, that does save my storage space and bandwidth. However, I have hours of other training video along with literally hundreds of other files, that are not intended for general public viewing/downloading. All of this is uploaded to my site and sits outside of public_html. I make those files available to registered users through a cms. That allows me to maintain control of my own files, on my own server, and protect them from general public access.
Uploading files to an external file host is fine for many people and many uses, but there are lots of very good reason for hosting files, large and small, on one’s own server.