There is a fundamental discrepancy or paradox that has been keeping myself, and many others, away from the stock market. Before I explain it, let me mention some selected popular questions on this site in which the consensus is that in the long term a broad investment in the stock market will yield a substantially positive average annual return rate:
In view of all this consensus, we can almost say that it has become "common knowledge" that investing in the broad stock market (sufficient diversification) on a long term perspective (several decades) is a very good investment strategy. More precisely, the consensus seems to be that there is some average annual return rate, say 3% (replace this number by something higher/lower if you prefer), such that if your investment is diversified enough and your timespan is long enough, the risk that your actual average annual return rate drops below that rate tends towards zero.
Now comes the first question: Why doesn't any (serious) bank offer a savings account with a fixed 2% interest rate for an unlimited amount of time?
After all, a large bank has the optimal prerequisites for diversification and holding stocks for many decades, and if the above is true, then they would still earn at least 1% of their customer's account values each year by essentially doing not very much except buying and selling some index funds according to what customers want to withdraw or pay in.
My own first objection to the question would be the following: If there is a market crash and at the same time a lot of customers want to withdraw money from their accounts, the bank might be in big trouble because the total value of the stocks owned by the bank could be less than what the customers want to withdraw.
However, I feel that this is not really an objection because even without the above "obvious product" banks will always be in trouble if their customers want to withdraw too much money at once.
What's bothering me even more is the
Second question: Why don't all banks borrow a huge amount of money from the central bank and invest it in the stock market on a broad, long-term basis?
As far as I know, banks can borrow money from the central bank at quite low interest rates (much less than the expected long-term average annual return rate of the broad stock market), in Europe that interest rate is currently even negative. So why don't all banks just buy index funds using this free money and just hold them forever, watching them grow in value?
Edit: After the first few answers (and some downvotes) I immediately realized that it was a big mistake to specialize the question in the sense that I only asked why banks don't do the "obvious" things, rather than having simply asked why no-one or no specialized company does the "obvious" things. I am very glad that in the further course of events my question was received in a slightly more abstract way. Thank you all for your answers and upvotes, earning me a gold badge with my very first question on this site! If one could only trade in those badges for their real world counterparts... ;-)