This is an interesting question. Is the question implying that most of the people who now invest in the stock market are not normal? Above normal? I will proceed on the premise that the question really meant 'should the average American invest' and go from there. There is no reason for anyone who wants to not to invest in the stock market, provided they have the necessary funds and the knowledge of what stocks to buy. However, the market can be volatile and very unforgiving, so it is best to study stocks for some time before investing very much money in the stock market. It is possible to make a lot of money and it is possible to lose a lot of money. The stock market is a good investment opportunity and can be useful to people from most income levels when approached wisely and cautiously. I know people in their early twenties who only work part-time summer jobs when not in school who are very slowly building a stock portfolio. It can be done, even by 'not normal' people.
Yes, I believe that normal Americans should invest in the stock market. I believe that there should be a way for regular Americans to learn more about the market and how to invest and do so wisely. It could be a great way for lower income Americans to make some more money if they invest in the right things.
As long as they take the time to research what companies they want to invest in and what risk tolerance they have I see no problem with the average American investing in the stock market, the stock market in general is a fantastic tool to help Americans achieve the amount of money needed to be able to retire successfully.
It is my opinion that normal American citizens should not invest in the stock market. I feel that most American citizens that are considered "normal" or "average" do not have an in-depth understanding of how the stock market operates, and this lack of knowledge would lead to a high amount of risky investments being made.
I don't think today's stock market is the same stock market our fathers knew. The stock market today is not geared to the average, "normal" person. Trading has become a science with computer software running algorithms faster than we can say "sell". If you aren't into "high frequency trading" , then you probably should stay out of the market.