Byteball did this. The problem is that when you give away coins for free to speculators, they are likely to sell them because they didn't decide to BURN anything (e.g. buy or do effort for it) for it, e.g. Auroracoin.
There's nothing wrong for them to sell it, on the contrary. The more a coin gets traded, the less it is concentrated in the hands of a few.
You don't need people to "invest" in something. The only thing you need is a large list of non-identical crypto-identity holders, so that the initial distribution is as large as possible. If it were possible to have, in one way or another, a public key of every person on earth, that would be the most ideal distribution. But we don't have such lists of which we know that they aren't manipulated. As such, the bitcoin address list looks like it is one of the best. There doesn't even need to be a correspondence between the AMOUNT of bitcoin to an address and the newly distributed coin. You could give a single coin to every existing address. Most of them are probably dead. But that doesn't matter. What is needed, is a large list of public keys, of which the secret keys are in the hands of as many people as possible.
You don't even need to TELL people immediately. You can have them discover their holdings way later. The important point is that whatever is used as public key, cannot be manipulated when the knowledge is out. It has to be a list "of the past".