It turns out, though, that we leave fingerprints on everything we touch. And many of the conveniences and indeed basic user experience we've come to expect leave plenty of markers of who we are for anyone who might be listening. This makes it easy for hacker news to remember who I am, and easy for advertisers to target ads, and governments to track individuals.
So yeah, tools exist, sort of, but require a lot of inconvenience. We've seen instances of ISPs inserting their own cookies on headers of outgoing customer traffic, meaning there are still times when your precautions don't matter at all. When I've thought about totally anonymous internet usage, my guess is that you need to go buy a fresh laptop with cash, and then only use it on large public networks, with good encryption...
The software which is currently closest to this is ricochet [0] which communicates directly between Tor hidden services. Since there is no central server, there is no one to record metadata (at least in a trivial fashion). However there is still a lot of work left to do before ricochet is something that could be mainstream. Also, some metadata can be leaked, such as when one is online, and (until proposal 224 is out) how much people are communicating based on the number of lookups on the hidden service directories corresponding to the service (since there is no randomness in the system yet, afaik, you can brute force values to get into the right place in the ring. I haven't read the Tor specifications in a while tho, so I may be wrong)
You could also use some sort of mixnet system, although you would probably end up leaking who is sending messages to their ISP. To stop the ISP from determining when, you could send o constant stream of encrypted traffic, although that would be inefficient. (I need to read more research on this)
However, weather people will actually use these systems is in entirely different problem.
Then, it depends where you sent it. Email goes to one person, so receipt of the message is seen on their ISP's side.
Yes the encrypted message is safe to be sent to the whole world, but there is no single public folder for "the whole world". That would be too many files. In order for the receiver to find what they wanted, they would have to browse the public folder to find what they needed, and this act of browsing strips the anonymity away.
The other problem is that you have to exchange the decryption keys with the person you intend to communicate with. You either need to physically give/mail them to the recipient (loss of anonymity in the case of mail), or else you need to exchange them electronically, which usually requires an A<->B exchange, or you can post your public key and let the recipient find it.
Basically, if you are a government watching all the communication from above, you can usually tell what path information takes, even if its posted publicly.
I think USENET and nntp came really close to fulfilling most of "single public folder for the whole world", but unfortunately has fallen out of popular use (and it needs to be popular enough to increase the anonymity) because it wasn't walled-garden enough to make money from.
Sure you could steal signals or go to starbucks (which has cameras of course ) a few times and maybe get away with it, but to do it reliably, on demand, is very difficult.