If crypto exchanges had a similar coverage, things would've been better. It'll be up to "crypto lobbyists" to do their thing for the good of the industry. Regulations are constantly changing, so fingers crossed investors will have better protections in the long run.
As far as I know, in order for crypto exchanges to get a license to operate in Japan, they have to able to secure user's funds so in case of the hack or something similar, users are safe. Thanks to Mt Gox, Japan learn their lesson and sooner or later that will come to other markets as well.Many won't be happy with stricter regulations, but at the moment, centralized exchanges bring worst of both worlds.
This kind of insurance would definitely not be free though. Because it's so new, and so risky (compared to say storing USD which has been done for over 200 years), we would be talking about a much more complicated kind of insurance, so the regulations would be much more complicated as well.
In the US, we have FDIC insurance, but that comes with a lot of strings attached. Being an FDIC-insurance bank is very expensive and cumbersome.
You are probably right about government lobbying: the way of modern capitalism is, "privatize the profits and socialize the losses"
. In other words, maybe Coinbase will try to get the US to insure them in case something goes wrong, and they will try to pay as little as possible for that insurance using their lobbyists.