Up until about 5 years ago I never even gave tire dates a second thought. I've also never had any trouble out of my tires except for the junk tires that came on my toyhauler.
Granted, I wouldn't really want to buy tires that are several years old, but it's possible I've done just that in the past. How many people buy tires without having any idea of when they were manufactured and never had an issue? My guess would be tons and tons of people.
However, I was recently informed by a poster that the date a tire warranty begins is the date of manufacture, not the date of purchase. I'm not totally sure I buy into that, but I have no information to the contrary. That would put a different spin on knowing when your tires were made.