It's not a terrible assumption to make. We just need to assume[1] that the decay events are independent, that is, every bond flips a coin every 500 years and if it comes up heads, it breaks, independent of what the other bonds do. That is, the process is inherently "local", individual bonds having no way of knowing what the other bonds are doing.

[1] It may be a bit worse in the long run, since if many bonds break, the higher order DNA structure gets damaged and that may change the rate of decay experienced by individual bonds (?).

half lives (specifically, the "decay" of any individual thing is stochastic but the aggregate of many molecules models exponential decay (in radioactivity. I have no idea what happens in a complex mash of DNA)