An analog for me is car repair. I could take my car in to get oil changes, have brakes serviced, etc. etc. Disregarding the money I save the reason I don't use those services is because those technicians and companies do not care about the quality of their work on my property as much as I do.
As an example, I was feeling too lazy to do a radiator replacement myself and so I took it to a big shop. Terrible mistake, when I got the car back they'd unplugged some of the sparkplug wires and forgot to plug one back in. There's no way they didn't notice the rough idling when moving it out of the bay. Even worse they wanted to say nothing was wrong until I had them pop the hood and pointed out the spark plug boot just sitting there.
Edit: To expand on this, the answer isn't buy a CDN solution. The answer is make CDN solutions so easy to implement that anyone can setup their own with their own hardware hosted in colos around the world.
... update their CNAMEs to point at a different company's CDN or a different video serving platform, and wait for the DNS to propagate
To me at least, the risk of a CDN or a video hosting service going bad or pulling your content is mostly the same risk as "colos around the world" going bad or pulling your content. Possibly a lower risk for most people - the chance of Cloudfront/Cloudflare/Akamai or AWS/Azure/GCE going broke or shutting you down is quite a lot lower than the risk of other smaller colo providers and your own hardware going dark. There's probably a smaller gap between smaller CDNs and cloud compute providers compared to rolling your own - but for most use cases I'd guess having a "cloud agnostic' design and ability to switch compute and CDN resources quickly and easily is a lower effort and more reliable way to reduce existential risk to your business.
I'm sure there are businesses who's risk estimates don't match mine - Darknet Markets for sure, probably "adult content" as well (given the observed puritanical zeal some of that industry gets deplatformed with). But for most clients and projects I've worked on in the 15-ish years since "Cloud services" became mainstream, owning hardware and leasing colo space would have been a totally misplaced cost/risk optimisation.(And I say that as someone wo used to do 2 or 3 trips a year from Sydney to colo facilities in the US and the UK with my luggage filled up with pre-loaded harddrives and toolkits to screw them into servers we owned on both US coasts and in London. I kinda miss the travel a bit, but I _totally_ prefer being able to get my phone out and provision new cloud "hardware" instead of hoping i had enough hot spare capacity somewhere, and ordering new hardware and plane tickets to fix disasters...)
Building your own infrastructure is like living "off the grid" with a wind turbine and a well and a composting toilet. You might have mitigated some risks but let's not pretend that there isn't an enormous cost in doing so.
And your infrastructure still isn't really literally "off the grid" of course. It's dependent on colos, network providers, etc. Sure, there's far, far less of a single point of failure than using YouTube but you're always going to be dependent on others to some degree.
Further, no one has the time or the money to do everything ourselves. To the upstream comment, I have neither the time or the energy to take on car maintenance. I have other things to do even if it means I spend more money and sometimes the shop doesn't do an optimum job. I'm not going to criticize someone who wants to do things themselves, but you have to choose.
Has had more uptime than Cloudflare.
FYI:
"An existential risk is any risk that has the potential to eliminate all of humanity or, at the very least, kill large swaths of the global population, leaving the survivors without sufficient means to rebuild society to current standards of living."
Source: https://futureoflife.org/background/existential-risk
Also: https://en.wikipedia.org/wiki/Global_catastrophic_risk
Your vps is perfectly fine so long as you're not serving traffic in China, India, etc. If you need to push data globally, need to handle very peaky traffic above the throughput of one machine, or need to have 99.9999% uptime, a cdn will look attractive.