Is this just about not being on YouTube or in general any platform? Otherwise I'd check out Vimeo for pure video hosting without the "social" part. There's a good reason that these platforms exist as they deal with all the encoding edge cases and different devices your users may use.
Vimeo (mentioned), JWPlayer, Mux, there's tons of options.
You could get away by hosting an mp4 file on S3, but you lose seeking, support for bandwidth-responsive quality/resolution, support for every device under the sun, and metrics.
And it may not be cheaper. I got a surprise AWS bill when someone hotlinked to test video files I was hosting so people can download them and use locally. That one oops could've paid for Vimeo Pro subscription for a lifetime.