While very large companies, who have their own online servers, still embed their website videos into their own web pages, most company web sites do not. The reason is that many services that host videos online have taken over that role.
One of the main reasons for doing this is the bandwidth needed to stream video. While viewing a streamed video only requires one feed, hosting requires a stream for every single person watching at a time. Even if the videos are watched at different times, they still result in an enormous amount of bandwidth being used. If this is all supplied by a single webpage, this can result in a costly web hosting situation
Services like Vimeo provide companies with the ease of hosting while having full control over their videos use, protection, copyrights and ability to be changed on demand. While many people still use YouTube for video hosting, because of the copyright issues arising from YouTube agreements allowing YouTube to resell the videos, private video hosting services such as Vimeo have become more popular.
Videos have become an integral part of company website and many businesses use video to display products and services as well as provide helpful videos for clients seeking more information or "how to" videos.
Video embedding is not the same as video hosting.
It is important to understand that all online video is not in a standard video codec. Each streaming service uses its own codec and each have their pros and cons when it comes to quality and bitrate. An embedded video which the website has internally stored as an H264 or MOV video will often be of vastly superior quality to the video hosting codec.
This is why companies who have the money to spend, will often host their own webpages on their own server with their own videos hosted internally and not on a hosting platform like Vimeo or YouTube.
When a company is hosting a larger collection of videos that do not need high quality, such as training videos or "how to" videos, these are often outsourced to video hosting companies.
If you intend to make "cinema" level videos, often the hosting companies simply will not provide you with the quality you are looking for. A good example of this is Netflix. They are able to provide extremely high quality video on a streaming services with millions of users. This is a greater achievement than many will know.
In order to have many people stream at the same time, the video bitrate has to be heavily compressed. This results in "blocky" video very poor contrast or dynamic range in the image. If you go to 4K video, this situation is even more complicated. It does not help if the viewer has a high speed line if the company hosting the video is not able to provide the video stream at a high enough quality that is still able to be distributed to multiple users without disrupting the stream to any individual viewer.