Honestly, I think it’s great: if it annoys people enough, they will move out from Chrome and install Firefox (or one of its forks) with good extensions for blocking ads on YouTube. It seems to be the only solution to break the monopoly of Google on browsers. So go Google, I believe in you!
Edge and Chrome are both closed source and owned by companies, so your comparison is just not valid. Using AOSP is certainly not supporting Google’s monopoly: AOSP is totally open source, was bought by Google a long time ago and they don’t own it due to its license (aside from the name maybe). Meaning you can still flash Android on a system without paying or using Google’s services or products.
It’s like saying you contribute to Google’s monopoly because you use Linux and Google (also) used it in its Chromebooks.
F-Droid isn’t the only one: I also like Neo Store, which has more than just the F-Droid repository and I think has a better interface. However, I think not all repo are 100% safe because F-Droid verify all the apps they have while Neo-Store doesn’t because it simply list known repos, which you can activate however you like in the settings.
Root can be useful for plenty of reasons: there are many apps which use root access to increase privacy, customize the system, restrict apps, manage battery charging, enforce firewall for apps and system, block trackers, backup the system, etc… I currently have 8 apps (if I don’t count all the lsposed modules) using the root privileges to do all of that but I also use it for other things like automation.
The only kind of security I want to have is privacy from my own apps installed on my system, something root privilege allow me to have. For the rest, I just don’t install any random program on my phone and I didn’t have any problem for years.
(and no, I can’t do any of that with shizuku or adb)
You have to give them a reason to get interested in the OS and the programs they’re using. I gave Linux a try because I was concerned about privacy and I wanted to use more ethical and user respecting OS and software than what I used at that time. Linux and the FOSS world was an obvious choice for me. Custom ROM on Android was sort of the bridge which allowed me to transition. If it wasn’t for that, I would still be on Windows and I wouldn’t learn that much on how an operating system works and what differentiate them, aside from the look. The fact they’re kids or that they play games have nothing to do with it: a lot of adults don’t know either what type of OS they’re using, despite it being in their best interest. The problem is that we don’t give or show them the reason they should be interested, or at least be curious about it and most of time, before people get a degree, we end up killing their curiosity.
As they play Minecraft, you can advise them to switch to Prism Launcher instead of the minecraft launcher, especially if they mod the game, it’s much better for that. It could be a good start.
Chromium doesn’t need Chrome to exist either: it’s a separate project and if Google doesn’t want to support it anymore, someone can easily fork it to continue having Chromium-based browsers. That’s the property of open source: anybody can inspect and fork it.