Pretty much the same as: Are banks safe? or Is Paypal safe?
When it comes to centralized systems, it all comes down to their integrity. If the developers are trustworthy, endorsed by the Government/prominent users, it could be safe from a ban.
Governments aren't banning coins based on their design.
Did you mean: "Can centralized cryptocurrencies survive even when the Government bans it?"
BTW, the idea is a great alternative to classic systems that requires more solid security like (Central) banks.
@mdayonliner (B) has a central body too, where did you get that image?
If those were Bitcoin Nodes, it will look like a haywire. (each dot should have a line connected to each of all the dots)
I think this is the most nuanced answer here.
While I'm absolutely a crypto supporter, it bewilders me how people here can sometimes parrot lines about centralization as this untenable thing when it's how we've been living in our modern lives. Definitely many things can be improved via distributed, trackable, and trustless processes where we cut out unnecessary brokers and middle men. But let's not pretend we live in some nightmare world where no one is accountable today.
Just like with any technology, time will tell which blockchain application and cryptocurrencies add real value to the world.