Should I stream media from my hosting plan?

I'm running out of space on my hosting plan, so I either have to upgrade to a more expensive plan, move hosts, or else delete a bunch of files. Most of my space is being taken up by media files (obviously).

Are there any compelling advantages to continue hosting media (video/audio) with my host? The only thing I can think of is reliability. I can be reasonably sure that my host will not delete my files or go out of business, but I can't be as sure about other services online (especially if they are offering free space). But I'm pretty sure youtube isn't going anywhere, so I'm comfortable using them for most of my video needs (or vimeo when I need to upload something longer). I also just read that archive.org will allow me to upload all my audio, and will even allow me to stream from their space. The obvious advantage of letting them host my files is that it saves me space and bandwidth.

Am I not thinking through this from all angles? What am I missing? The choice seems pretty obvious to me.

Perhaps it depends on the websites that you are hosting and the media to which it belongs. For instance, if its important professional work, the idea of using YouTube etc might be somewhat plausible, but perhaps not particularly encouraged at the same time.

There are many other hosts as well that will let you keep quite a few GB of files, and let you stream them too. However, so long it isn't copright stuff then they have nothing to say