These are not "streaming boxes" in the sense you are talking about. Their appeal is that they come preloaded with chinese pirate streaming apps. Traditional streaming boxes - Apple TV, Fire stick, Roku - are not affected by this, though if you want privacy-focused Apple TV is the only remaining contender, and with Apple's continued descent into advertising vendor I'd guess that one is not long for this world, either.
I’m sure you could. At what point do you just rip out the thing that is trying so hard to work around your control of your network? An Apple TV doesn’t cost that much.
Apple TV is currently the best balance of privacy and convenience. The only way to get more private is using a PC, but that limits the resolution for most streaming services to 720p or 1080p.
If you want actual privacy (rather than promises from Apple or Google), what you need is a mini-PC running Linux with the Plasma Bigscreen DE. You then use a Web browser rather than invasive "apps" for your streaming. For Youtube, there is VacuumTube (an improved Youtube Leanback client). The main limitation is capped resolution on some commercial streaming services. I believe Windows does not have that restriction, so a VM could presumably be used for streaming (I have not tried).
I'm increasingly being convinced the only way to do that is you do a media pc nuc. The problem, of course, is you probably won't have the netflix app. It's painful to setup such a box to stream from various services.
I tried to look at setting up an stripped down privacy-focused Android based box for Netflix, but ran into issues. Seems like you need to be spied on to run Netflix.
The Onn TV devices from walmart seem fine, baseline google tracking not-withstanding... but no residential proxy or botnet participation without you knowing! You can just block them at the router and stream content locally.