This thought has also crossed my mind.
Possibly use the hyperbolic tangent in the generation curve. If used directly you could choose the time of 50% currency minted arbitrary and it still would work. And the scaling can be used to choose the slope. Also it could be made asymmetric by using it on any polynomial of your liking.
The problem is, it will cause a fairer distribution as long as it fits the adoption pattern, which is absolutely unknown.
Looking back now, you could say that ease-in-ease-out would have caused a more homogenic distribution since it fits the historical rate of adoption, but that's not quite right for two reasons. First, by changing this initial condition, you alter the adoption pattern, which invalidates our initial conclusion. Arguably it would result in the same heterogenic situation as now, just with a different scenario. People who bet on the system's success always get the biggest cut, and if the system fails they always lose the most
*. Second, we know Bitcoin's history, but we still don't know its future, so we really don't know where in that graph we should be standing.
I think by not trying to guesstimate the adoption pattern, and adopting a generation rate from the desired quality of the currency, Satoshi made the best choice.
(*) There is also the argument that the initial miners didn't invest that much, so their gain is unreasonably disproportionate. I don't believe this is true. If it was, we could now create infinitely many alternate currencies, and someone investing equal mining power in all of them would eventually profit. The reality is, there are a lot of things you can do with your time and money, and very few of them will be worth it. And an obscure crypto-anarchic fantasy is not an obvious choice.
