Banks perform the essential function of getting money from folks who have it (savers) to folks who need it (businesses, people buying houses, etc.) Shut them down for two weeks and see how the economy seizes up and your question is answered.
A better question would be, should this essential function be separated from that part of the bank (if any) that trades for its own accounts with the goal of making a profit? Perhaps, yes.
If as an "ordinary person" you want to partake in the bank's profits, buy shares in the bank. If you are covered by a private pension plan or invest in a mutual fund for your retirement, odds are you own some shares in a bank already.