A VPN, whether public or private, will not hide your traffic from the government.
Through statistical analysis and network protocol heuristics you can identify all sorts of things about bulk internet traffic - where it's coming from, where it's going to, the most likely content it's carrying, the application used, even a specific user's connection. This works over multiple network hops, encrypted, on a single tap of a large switch (though multiple taps spanning the network path work muuuuuch better).
There is one good use for a VPS, though - store-and-forward network traffic. You use a remote VPS to retrieve and store content, and at a later time, download the content in bulk (or upload, same difference). You can change both the size and the form of the content before the bulk transfer, making it much harder to identify. You can also use different network paths for connecting to issue the download/upload commands, and connecting to transfer it - Tor comes in handy here.
Through statistical analysis and network protocol heuristics you can identify all sorts of things about bulk internet traffic - where it's coming from, where it's going to, the most likely content it's carrying, the application used, even a specific user's connection. This works over multiple network hops, encrypted, on a single tap of a large switch (though multiple taps spanning the network path work muuuuuch better).
There is one good use for a VPS, though - store-and-forward network traffic. You use a remote VPS to retrieve and store content, and at a later time, download the content in bulk (or upload, same difference). You can change both the size and the form of the content before the bulk transfer, making it much harder to identify. You can also use different network paths for connecting to issue the download/upload commands, and connecting to transfer it - Tor comes in handy here.