I bet that's a big part of it. It's indicated canonically, the Chief only had his Mark V a few months and by the start of Halo 2 it was falling apart.
There's also the issue of just how technical this equipment is. Running newer firmware and supporting armor abilities/armor mods/support upgrades/Spartan abilities/whatever have been implied advantages, and they might just be the beginning of it. Cell phones are a good parallel I think. Smartphones now can do things out of the box that were blatantly not doable a few years ago, so as much as you might love your old phone, on the basis of straight-up features, it makes a lot of sense to upgrade.