In fact, it's pretty routine. Don't have the source at hand, but somewhere around 1% of all landings (at airports with ILS) are autolands.
I think it was Boeing that even requires at least 1 autoland per plane every 30 days or so.
You can find videos of this on YouTube. Completely hands-off.
This is a competence you do not want to lose.
It's also the case that you can have a whole approach setup in your flight computer and at the last minute the controller gives you a runway change. You could drop your head down and start typing a bunch info the FMC but you're generally better off just disabling auto pilot and manually making the adjustment.
But two interesting data points from the Wikipedia article I linked are that the first aircraft certification for ILS Cat III was in 1968, and Cat IIIB in 1975.
And IIRC by the 1980s, autoland was already a pretty common feature.