When cars fail their MOT and become "scrappers" the tyres are not usually wanted by the scrap dealer. Note also that otherwise good cars can become write-offs because of a slipping clutch or a broken timing belt if the owner is not mechanically minded and Murphys Law dictates that this will probably happen when the car has recently had new tyres. Quite frequently scrap cars will have an unused spare wheel, nothing wrong in re-using that.
As to worrying about blowouts, nowadays these are quite rare. In any case the really important thing is to know how to deal with such a problem. In particular DON'T HIT THE BRAKE. Many years ago the scientist Newton postulated that "any moving body will continue in its path of motion until acted on by an external force" (or words to that effect). The correct thing to do after a blow-out is to INCREASE engine power slightly to counteract the drag of the flat tyre then use the steering to regain control. One can then lift off the accelerator and slow down gradually.
Some years ago whilst travelling at speed in a supermini I noticed a thump from the rear. I mentioned that something was making a noise - maybe the tailgate wasn't fastened. Driver stopped, couldn't find any problem (it was dark) so drove off even faster in a bad temper to make up for lost time. More thumps occurred then the car lurched and a humming noise began. The humming continued for about a mile so I assumed that the road had been roughened-up ready for new tarmac. A little while later the driver must have seen sparks in the mirror because he suddenly stomped on the brake pedal. Bad mistake! The emergency stop on three tyres and a rim set the car spinning like a top. The car did three complete spins then went of the motorway backwards down an embankment. Lucky to walk away from that. A less bad-tempered person would have coasted to the hard shoulder and fitted the spare, no need to wreck a good car. Incidentally the car had been professionally maintained (hahaha!) and as the front tyres were the only ones that wore to any extent, they were the only ones that were ever replaced. The rear tyres were the originals and several years old. Please note that with front wheel drive cars the new tyres always go to the rear.
With used tyres one must weigh up carriage charges and fitting charges. If the tyre fitters charge for stripping off the old tyre, new valve, fitting replacement tyre, balancing, old tyre disposal charge (all plus VAT) then the "bargain" tyre won't be a bargain at all. Some extremely strong farm hands can however change their own tyres with just a couple of tyre levers (after practicing on tractors they find car tyres quite easy!) Bead breaking can be done either with a vice, a jack and heavy trailer, or by using the tractor and plank method.
As to the robustness of wheels and tyres, the problem is the road and obstacles in the road. In Devon and Cornwall many roads have neither verges nor pavements. Instead there are "Devon Banks" made from stone and earth. It is quite common for stones to fall out of the hedge and lie in the road. These stones cannot be seen at night when one is dazzled by oncoming traffic. Amazingly the wheels and tyres usually survive unless one is running ultra-low profiles on alloys. (Allegedly BMW M3s are notorious for getting smashed wheels and just driving over a pothole can do it). Lastly just remember that car tyres are rated to carry their sidewall rated weight at the cars top speed. At lower speeds the safety margin increases so with 150 mph tyres and a 70 mph speed limit, blowouts should never ever happen. Old trailers (not HGV) are different as often the tyres are barely adequate. Some trailers get fitted with agri tyres only rated for 20 mph and these will shred for a pastime if towed with a decent turbo-diesel. Needless to say the agri markings soon wear off. Caravan tyres can also blow, especially if the tyre reinforcement is not nylon and steel. Everything is relative but jetliners often use remoulds!