> Europeans basically keep their savings in bank savings accounts.
USA is not much different. The wealthiest 10% of the U.S. population holds the vast majority of stock market wealth. Recent data shows this group owns around 90-93% of all stocks, with the top 1% controlling about half of the total household equity.
Many people hold cash in savings to prepare buying a house, paying for a child's college and more. IMHO, there is also less short-term need to invest your money as an adult.
If you're happy with your job and don't need the extra money (or risk), then why invest in the stock market?