I'm writing this off the top, so you are going to be able to find all kinds of flaws in this idea, but here goes.
How about a new crypto called CaptchaCoin, that starts out with zero coins in it. There is no mining as we know it. Rather, the mining end is set up like a captcha, yet a captcha with extremely random settings, so that it is as close to TRUE random as possible.
It would work like this:
1. You launch the CaptchaCoin program on your computer;
2. You go to the CAPTCHA screen in the program;
3. You type in the long captcha that you read on the screen;
4. If you typed it correctly, when you hit ENTER, you get a coin;
5. A new captch pops up on your screen, and you start typing again;
6. Coins are loaded into the non-Bitcoin blockchain, in Bitcoin fashion, added to your CaptchaCoin address, upon Internet connection.
If you want to become rich, you need to learn how to type faster, and how to talk friends and family into working with you on the captcha project. Your kids can type while you are at work, and you give them a percentage.
100% inflation is automatically built in, because the more coins are captcha/created, the less all of them are worth. The more people who work the program, the less your coins are worth. Because of this, you need to trade your coins off frequently/regularly for gold, or land, or cars, or fiat, or whatever, just so there won't be loss due to the built-in inflation.
This kind of coin would cause everyone in the world to be in competition with everyone else. Competition makes for popularity and fame. Might even be able to make audio captchas for the deaf. Because it is easy to mine, there would be no end to the numbers of people who would want to join in. Yet the captchas could be built in such a way that it would absolutely take a human to analyze them. Government couldn't stop it in any way, because people would run right around ALL governmental authority, one way or another.
There would be no advantage to storing (hoarding) the coins. Their value would drop continually if you didn't trade them for real products of one sort or other. Bitcoin wouldn't die, at least not right away. So, CaptchaCoins could be traded for bitcoins.
Soon fiat would be entirely out of business. Trade would abound because of the inflation factor. The whole world picture would change.
Now, some of you thinkers and gurus, take this idea and work out the flaws, and program it into reality. But do it fast, because if you don't, somebody else will beat you to it.
EDIT: Hey, it took Satoshi years to develop Bitcoin into a working operation. He needed the help of the devs. Something like CaptchaCoin won't happen overnight, even though it could be built much faster than Bitcoin, because we have the Bitcoin pattern to follow.