The most important aspect of expiration isn't even the plastic, although that is scary. Generally, you can be sure their is enough of a buffer built into the calculation of how fast the plastic will break down that the seat isn't going to crumble anywhere near the expiry date.
The real issue is that technology changes very quickly. Both in car seats and in cars. A car seat made 15 years ago may not be compatible with things like side airbags, LATCH, seat belt placement, active head restraints, and other commonplace features of modern cars. They might be, but they haven't been tested for this because these things didn't even exist when the car seat was made.
Then you get into the issue of how the manufacture is no longer responsible for continuing to test seats and release recall info once a seat expires. The components are engineered with a certain life span in mind, and they test to make sure they hit the mark, but they don't test to make sure they go significantly past the mark.
Finally, car seats have lots of parts. Those parts get lost or damaged over time and manufactures stop carrying replacement parts after awhile.