Okay, so now you’ve downloaded the entire chain. Does that seem safe to have in your possession in this scenario? Even if I have the storage, I would not want to find out that someone else had uploaded something illegal when the police search my computer/phone and I have to prove to their satisfaction that I didn’t know.
If you don’t download the entire chain, your traffic connecting to certain nodes and downloading certain sizes can be enough to track you - there are academic papers about using this to figure out what movies you’re watching over HTTPS – and that’s assuming that you don’t learn the hard way that the fast server with all of the underground content is the secret police’s honeypot.
This is all probably moot in any case because it’s tricky to build something like this which never does DNS resolution, connects to a suspicious server, etc. The average user is going to have a very hard time avoiding mistakes like that, and that’s assuming you don’t have police informants encouraging unsafe opsec or use of treacherous apps — real things which happen to dissidents and activists all over the world. Remember Citizen Lab’s report on the use of NSO’s malware to go after supporters of a soda tax?
What bothers me most about cryptocurrency proponents are that most of the claims are being made by people who will not personally suffer the consequences of being wrong if someone follows their advice. If you care about people in dangerous legal environments, that really needs to focus on changing the system rather than advocating use of electronic systems which even experts cannot use safely in those environments.