Is this because of the rubber drying out?

My understanding is that this is why tires need to be replaced after 5-6 years and are not safetiable thereafter. The dried out rubber is much harder than when it was first made and no longer grips the road as strongly.

Tires actually dry rot from ozone exposure, theoretically, if you store a tire in an airtight container - it won't have a problem.

If you drive 10-15,000 miles a year (about average), your tires will probably be bald anyway in 5-6 years

Yes, largely, the rubber hardens or has otherwise become worn