Storage (and bandwidth) is expensive, that’s the whole reason. Lemmy is community financed, and the amount people donate is not enough to add video storage. Theoretically it’s perfectly possible, Lemmy instances just have it disabled.

For now, the only possibility is to host externally. I self-host a Lychee instance on my server, and use that to permanently share my content. But there are free services available that allow hosting videos, to which you can then share the link.