Minorities will participate less because I believe they statistically are less likely to already have an ID. Also you must recognize that most of the people who do not have an ID are the extremely poor, elderly, and rural people. They may not have money to spend on an ID, they may not be able to leave their homes due to health, they may not have access to transportation. It is to these people that ID requirements becomes much more of a burdensome than to you or me who are in relatively good health, have easy access to transportation, and probably already have an ID anyway. You addressed the money issue (assuming the states all agree to your free ID idea), but you need to provide solutions for the other issues as well. We shouldn't add more hoops to jump through just because we will make everyone jump through the same hoops. Now if voter fraud becomes a bigger issue then maybe we can justify erecting higher barriers to voting but at this point, I just don't see the good outweighing the bad.
If you have to fill out paperwork for any part of the government, you are navigating bureaucracy. It doesn't matter if it is for driving a car or opening a liquor store. It is not a pejorative, it's just the definition of bureaucracy.