The chance of your self hosted server going down, being hacked, catching fire, etc is infinitely more likely than google drive being shut down so fast you can't switch to something else.
At this point the advice is moving towards "Don't even have a video if you can't be bothered designing a CPU from scratch to host it on".
Keep a local backup by all means but it's far more likely the local copy will get lost than the google drive copy.
I'm a little skeptical of that, especially in the scenario that it's a "don't want to look at it much" situation. I've had VM's running for many, many years in an autoupgrade scenario, and it tends to just work. And the security risks are often overstated as long as you tried to minimize attack surface; so; for instance I for a while tried to track all related security issues - and at the very least 95% are irrelevant, and that last 5% is more CYA uncertainty than actual belief its relevant; I didn't find anything positively certainly relevant.
Obviously, if your website is running a complex stack this is fairly infeasible (good luck keeping a complex web-framework secure without vigilance!) But if it's just a static site... and static sites are the fair comparison to google drive.
The issue with google drive and similar products is that they're actively - very actively - maintained. Stuff doesn't just break because it's taken offline, but because there are changes in terms of service, there are automatic deactivations for inactivity, there are plain old incompatible upgrades, etc, etc, etc.
I mean - I totally support people starting with the minimal effort (which is surely some freemium service like google drive), and leaning to live with the limitations - but the risks of a server (whether physical or otherwise) if you're similarly conservative and willing to live within constraints not unlike hosting on drive seem overblown - people talk as if servers burn down all the time, and hackers crack everything, but nothing could be further from the truth - those are exceedingly rare circumstances. And for many things, those risk are just OK. Don't keep your only copy of the data on the box, and don't keep private stuff there, and if lighting really strikes - it's not so bad. And both strategies will need a little TLC once and a while, that's just the way it is.
I have seen plenty of these servers left unattended for years and they all build up weird issues like time drifting out of sync, log files filling the disk, hackers somehow getting in and setting up crypto miners.
None of this is stuff the average company needs to deal with when youtube works just fine. I'm sure you can list out all the ways to avoid those listed problems but that just shows how much work and knowledge is needed to pull this off while anyone can use youtube.
Sure, and I certainly would recommend people start with an off-the-shelf solution like google-drive. But that recommendation is based on precisely that - you don't want to need that expertise, nor risk screwing it up. But it's not based on the fact that it's actually pragmatically more reliable (or less ongoing effort) to host on something like google drive.
Self hosting is as easy as having the videos on a single location on the shared drive. Most companies that have employees use computers use internal shared drives like this to share files and VPNs for their employees at home to access them outside of the network, and have their own IT departments to handle all of this.
The Google drive could be deprecated at any moment