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.

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@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)