In the five homes I've owned over the last 30 years, I have never had an
expansion tank on the hot water heater. My daughter just bought a home (new
construction) and it has one. Did something change? Do I really need one?
It seems to me that any expansion of the water in the tank would just be
pushed out the cold water inlet and pressure wouldn't increase. What am I
missing?

It depends on what's upstream of the cold water inlet.
If there's a checkvalve before there's a pressure tank,
then you ought to have an expansion tank.