The reason sharedrops that "simulate mining" work is because all of the early adopters etc are miners. Most of the die-hard types sitting on forums have at least dabbled in mining and believe it to be "fair". There is nothing special about mining that sells a distribution except the existing adopters have mentally bought in.
They've put their capital into mining equipment so now they're a middle man selling hashes and taking the profits and paying the electricity providers. This is not much different from paying for shares directly, people just need to have it explained to them.
Mining is also labor intensive so it keeps large capital from showing up and just buying in. This is probably the one biggest thing people need to avoid in the longrun, the perception that the guy with the most money at the start ends with the most money. Lots will disagree with it, but this is probably the biggest perception at play when people don't like POS. An "unfair" distribution. Mining is only marginally more fair because it requires labor to set it up.
The point is to attract interest from miners and bring them into the Bitshares ecosystem. I think this is a good way to do that.
Depending on the hashing algorithm or kind of mining some people might think they'll have more advantages. They'll spend more of their hashing power in the Bitshares ecosystem which is good. There will be plenty of new coins which are ASIC resistant at least for a while and people will mine them (also some coins will be for storage, bandwidth, etc).
Long term you can replace mining with any number of serious games which are based on attention. Viewing advertisements could be proof the person is interested and generate enough revenue if we wanted it set up like that. The point is that the sharedrop or faucet has to be based on proof of interest, the serious game (ritual) doesn't matter too much as long as it's not so trivial that a bot can do it or that it can be gamed.
So think of the serious game as just the game people play to show interest and participation. Some people are expert miners so they know that game but an ASIC miner will not have an advantage over a storage miner. There will be many different kinds of mining and that diversity for a while will keep it fair enough until we reach a point where the industry matures or it gets centralized.
This is worth further discussion because I basically agree with you on the "pay-to-win" problem. Newcomers will not think it's fair unless new serious games are continuously devised.