There's no simple answer to this question. There are a lot of variables, and there's a lot we still don't know. A few points:
- Generally these wear recommendations are concerned with midsole longevity. If the outsole is worn through so you have no traction, or if the upper is shredded, you will obviously know, and you can judge for yourself what's still runnable. I always replace shoes when the uppers tear, simply because I think it looks bad and I have the money. When I was younger, I wouldn't have worried if my toes were poking out.
- Different midsoles have different life spans. A lot of recommendations are based on EVA foam, which is increasingly falling out of favor. Boost foam (really all the TPU foams) is unbelievably durable. Other foams, like the blown pebax used in the Vaporfly, appear to be less durable than EVA.
- Shoe foam loses its cushioning properties quickly, but then levels out. By 500 or 600 miles, the midsole will be compressed, and will probably only have about 50% of the travel (how much it compresses and expands with each impact) that it had when it was new. But it won't get any worse than that. Many people who wear the Vaporfly have noticed that the shoes very quickly stop providing the amazing cushioning they had when new, but because they're so cushioned to begin with, people are getting a lot of miles out of them. (A half-dead Vaporfly is still a pretty sweet ride!) This is why some people are able to go for multiple thousands of miles. If you think the shoe feels fine at 600, it's probably not going to feel much worse at 1000 or even 2000.
- Thicker shoes and "supportive" or "motion control" shoes can change their shape with wear. Even if the cushioning of a shoe is still adequate, sometimes the midsole won't compress evenly. Eventually the shoe bed can have a different shape than when it started off, and this can affect footstrike patterns. The problem is worse with old school medially-posted shoes, because the different densities of foam are guaranteed to wear unevenly. By contrast, a shoe with a thinner midsole isn't going to change shape much because there's less foam to compress.
- There is no evidence that running in older shoes is likely to increase injury. Though, as with all sports science, take lack of evidence with a grain of salt. The research is always far behind practice. If anyone tells you that you're being stupid for not replacing your shoes sooner, you can safely ignore them.
- It does appear plausible that running in old shoes could increase soreness and cause you to run slower. Cushioning reduces biomarkers of muscle damage such as creatine kinase, and cushioning also increases running economy. If a shoe weighs the same but cushions less, you will almost certainly run a (tiny) bit slower in those shoes.
- There is also evidence that rotating shoes decreases injury. Some people have mistakenly suggested that rotating shoes allowed the midsole foam to "recover" between runs so it lasts longer, as though it were a human muscle. The real reason (probably) to rotate shoes is that different shoes cause minute differences in stride mechanics, which helps the runner avoid overuse injuries. Many people also prefer to have a rotation going so that they have at least one pair of newer/cushier shoes available at all times. It can be a useful point of reference when you're deciding when to retire an older pair.
So the bottom line is to experiment and figure out what works for you. Replace shoes when you no longer enjoy running in them. Don't be afraid to retire a pair early if you're no longer digging them, and don't be wedded to some arbitrary number of miles.