Your argument makes sense, and I share your feelings on an emotional level, but at this point, the whole argument can be reduced to "sharing video files streamed from google drive is an equivalent of hosting a video on youtube, so the same rules apply", and that's hard to beat.
If you want to store whatever material you want for personal consumption, you are welcome to. But if you enable sharing, that's when all those extra rules start applying, because you are effectively turning it into a personal youtube that is still hosted by google, and DMCA strikes and other stuff will apply just the same.
Similarly, you can make backup copies of a DVD movie for yourself by burning them onto writeable DVDs. The legality of it is dubious due to copyright law being plain awful at times, but you won't get prosecuted for that if you truly had it only for personal backup reasons. The second you start distributing those DVDs in massive amounts to people, you start inviting a pretty legal trouble to your doorstep.
Mind you, I absolutely disagree with the ban of both the historical footage, as well as the whole google account just because of that footage. However, I do believe that making video public via a shareable link or otherwise puts it in the territory where content rules similar to youtube might get reasonably applied.
Then logically, why should it be available ad free either?
I don't think so.
Lets say you and I opened a joint safe deposit box at the bank to share USB drives together with movies on it. If the bank found out, they wouldn't be required to drill it open and scan the drive to make sure none of the movies were copyrighted. This is google drilling open the safe deposit box because someone shared the keys, and they think there may be a movie they don't like there.
Legally, you are 100% correct. The law doesn't require the host to do anything until a DMCA strike is received. But YouTube has its own rules, which is fully legal as well, as long as they are more restrictive than the law (e.g., establishments prohibiting alcohol inside are allowed, even though alcohol is legal; establishments allowing crack cocaine usage inside are not allowed, because crack cocaine is illegal).
And YouTube decided to take proactive approach here. The reasoning for why doesn't matter to the point at hand. The fact of the matter is, YouTube took a stricter approach to DMCA moderation and tends to not always wait until the video receives and actual DMCA strike.
I actually think that not making a distinction between publishing to the world and sharing with a small group of people is the biggest source of unreasonableness in all of these debates.
When I'm interacting and sharing with a few people I know or who I just met, I expect companies and governments to stay out of it (unless there is a criminal investigation overseen by a judge). I don't think that's unreasonable at all. It used to be the status quo until not very long ago.
Everything from political activity to copyrights can be discussed in a far more sensible way if we make that distinction. As soon as we erase that distinction, which has sometimes happened because it's the default with some technologies, everything becomes essentially unsolvable.
E.g, I don't want to defend the right to anonymity of someone who directly and systematically influences entire populations just because I expect to be allowed to do the equivalent of talking to three strangers in a pub without showing ID.
Google knows how many different people access a particular piece of shared content. They should just set a reasonable threshold before unleashing their crude algorithms. 2 is not a reasonable threshold. How about 200?