I was running on a sidecar so had 'stabaliers' but I do find it varies according to who made the tyre, and when, some are so grip focused that for instance my dads bmw ran Conti Tour tyres, it wore the last one out in 3k miles, previously they had lasted 7k + per tyre dad complained to Continental tyres and was told the market demanded more grip, there was nothing wrong with the tyres before and 3k from a rear tyre makes a bike prohibitive to use.
I know what you mean about old tyres being sometimes very dodgy to ride on, my Suziki Gs125 was a 1982 bike, and when I first had it had her original bridgestone tyres, probably still with 90% of the original air, they were truly horrid in the wet but as a poor student I had to keep using them and the bike needed carefull handling being on 20 year old tyres. Drum brakes both ends were no help. I eventually saved up and bought a complete front end off a disk braked bike and grafted that on.
The seat of your pants will soon tell you if the tyre is too old to be much good even in the dry if you know that feeling, or just dig a thumb nail into the rubber, the feel tells a lot. Proper storage of tyres makes a major difference to their shelf life.
