They are absolutely no where close to a virtual monopoly. Anyone can upload and stream content online, and probably millions of websites allow it now, without exaggeration. What they have is a prefab audience. There are no considerations needed for free speech whatsoever.
If you want to influence their moderation habits, you need to be their customer or better yet, their shareholder. As just another leeching user, your voice means nothing to them and frankly that isn't problematic. 10,000 leeches won't influence them the same as one paying customer. I can guarantee that. And again, if you're just a leech then it really is no wonder why they wouldn't listen as a for-profit business.
There are troubling bits about lots of platforms and media outlets and companies, but that's not an excuse to twist up legal terminologies like monopoly or free speech in order to make weak criticisms. Doing so weakens the framework of law more than it does influence YouTube at all. Because that framework of law is only as valid as we use it. Countless examples of that problem abound - virtually the entirety of the Trump presidency is an example of why misuse of the law in common discussions among people is actually very dangerous. That's been a sticking point for me for a long time, and it's more important as years go by. So I'm gonna call it out, especially when it's happening on "my" team.
If you're gonna make accusations where we actually have legal recourse (like monopolies) then you need to understand them. There is no where close to a real monopoly in YouTube.
"Warnings about explicit content work" is a new take to me. The history of such direct warnings tells us otherwise. At one point there were bands dropping F-bombs on albums just to get that sticker. Because it increased their sales and visibility.
The Streisand Effect is real, in big ways and also in these small ones. I'm not saying don't try, but I'm telling you it won't ever work the way you think it will.
What's interesting is that the MPAA Rating system itself was a compromise from the industry with the government to avoid the government stepping in to control content. That's where it started. Seems eerily similar no? It's not coincidence. But that's just another example of the point I'm making too: originally they rated porn movies "X" and agreed these wouldn't be in the industry- controlled theaters. Porn movie producers took it as a badge and began labeling their movies "XXX" and leaned into it so hard, the MPAA had to change the distinction to something more innocuous, "NC-17." But the cats out of the bag, even today every 11 year old kid knows what XXX means. The warning became a siren call.
Warnings are just the Streisand Effect, so don't expect much of them.