These are my personal experiences and observations. Even on a daily driver, I never keep a set of tires beyond 4-5 years, regardless of how much tread remains. I've found the rubber gets hard and tends to slip on any wet surface, even on leafs. The sidewalls and likely the metal belts tend to deteriorate and as suggested, cause tire destruction - not safe at any speed.

Specialty tire shops can supply almost any variety of vintage replacement tires. I have original bias-ply BF Goodrich 5.90 x 15 on my vintage Volvos. The rubber used on these "new" tires seems to be longer lasting than the original rubber compounds. One supplier in particular Coker Tires even make radial tires with the vintage wide whitewall.

Driving a 50 year old vintage car is enough of a challenge (mechanically speaking) to have to worry about the rubber your valued car (and body) are running on.
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Cam a.k.a. CVOLVO.COM