3% is becoming more common as of the last few years, at least in the US. I know several banks off the top of my head that offer 3.5% or higher (and more if you are a new customer) for their savings accounts. I would persuade people who use banks that haven't moved on from near-zero APY to move on themselves.
The rate goes up and down with inflation, high inflation, high interest - low inflation, low interest.
But even then, yes some banks still offer no or 0.5% accounts.. because they can, and many people can't be bothered to figure out a better option, or "trust" there bank and don't want to move. (or the bank has high interest account, but make it complicated to use)
I'm definitely at the point where, if not sticking money in my mattress, I'm keeping a lot in pretty safe investments. Did sort of an equity housecleaning a couple years back and consolidated some investments, in part to make them easier to track and manage.