Truthfully,
We all know new or nearly new tires fail. Putting on fresh tires is not a guaranty of no failure or damage.
You do know the old ones have proven that they were built right and only will succumb to time and the elements.
If the car is garaged out of the sun, tires will last a long time.
Check for cracks, bulges or bubbles before you make the call to buy or drive on.