Yes car tires should be replaced especially if they're 10 years old or older. Even if the tread is still good the rubber starts to weather check and deteriorate and can lead to a blowout.
10 years is the maximum you should use a tire before changing it out no matter how much tread is on them.
Tires are expensive but your life is worth so much more than the money you'd spend on new tires or a hospital bill if you managed to survive the wreck due to a tire blowout.