.... and don't tell me this is not possible....
To answer this part, it's certainly possible with custom work, but I suspect there are quite a few very good reasons why it hash't been done already.\
One reason uploading videos onto the internet (and onto forums) is not as ubiquitous as uploading images is simple: file size and bandwidth. Your average common-or-garden picture will be in the realms of a few hundred kilobytes, give or take, perhaps stretching to a megabyte or two for really big images or complicated GIFs. Videos, however, will be anything from a few megabytes to several hundred megabytes, depending on length and quality.
To do the math, let's assume I upload a 500kB image and a 50MB - or 50,000kB* - video into a thread. For argument's sake, let's also assume 100 people visit the thread in question, and they all load the image and load the entire video.
So, firstly, the images: 500kB x 100 is 50,000kB, or 50MB. In English, this means that 100 people downloading the 500kb image results in 50MB of bandwidth usage. This is a pretty big image, but typical of an image uploaded straight from a smartphone without processing.
Next, let's move onto our short video: 50,000kB x 100 is 5,000,000kB, or 5GB. Yes,
5 gigabytes. So a few small videos on your forum can easily make a mess of your bandwidth bills. There are also other, server-related problems with transmitting videos, but I am not familiar enough with this to speak with any authority.
The thing is, really, YouTube and Vimeo are both established, well-used to hosting videos, and most importantly, free. In my eyes, I don't personally see a compelling reason to self-host my user's videos over just allowing them to upload to YouTube, which is what they already do and are well-versed in.
*For the sake of simplicity I'm assuming a megabyte is 1000 kilobytes, as opposed to the more traditional 1024 kilobytes. Both are technically correct.
