If rates or yields remain positive for retail products, what's to stop hedge funds / companies with lots of cash / banks, from investing in those same products? Yields may be positive on paper, but I would suppose that fees will hide the fact that actual returns will be negative. Set up maximum account balance limits and you restrict investment by the non-retail crowd. Then again if these products are actually making profits for the small guy, what's the seller's incentive to keep providing them?
Because you can't buy $1 billion in individual cash saving accounts; there isn't a supply of them and a bank won't sell them to you. When you have very large sums your options of what you can buy and kind of the returns you can expect change. A small investor with $10k can experience greater volatility in their returns (good and poor), and can just go ahead and buy Apple shares without the FT writing an article about it.
Also, the base rate is only really encountered directly by Banks that have accounts with central, in the case of the US, or regional central banks. A normal company and even very large non-bank firms don't typically have accounts with the central bank. For consumers and most businesses the interest rate set by the fed is more of a benchmark that ends up being used to help calculate the returns of other products.