It's not a requirement, it's just that it tends toward it naturally due to the asymmetric addressability. As long as there are two or more global addresses available to the public on which to run STUN, UPnP, etc, there will be "competition" but it is immeasurably weak compared to what would be possible with direct (non-NAT) addressability. In an environment without those obstacles, systems are naturally designed in a P2P way - simply from the need for scalability.

Case in point A: Skype leveraged an initial P2P design at a time where direct addressability was the norm (and there were many freeware alternatives that allowed direct dialing)... Now that Skype has become dominant, it has switched to a centralized infrastructure 1) because it's owners can (it makes administration, censorship, and surveillance easiest), and 2) because a P2P model no longer makes sense with most users relying on their centralized bootstrap servers.

Case in point B: Dropbox and similar services have replaced self-hosted FTP, I would argue, simply because noone wants to maintain static port mappings and Dropbox is easier.

Even without other incentives, the presence of NAT is a centralizing force that - taken to the extreme (such as with carrier NAT) outright precludes P2P - and that is undesirable. In an Internet with NAT (or any other violation of the end-to-end principal) all systems suffer the same fate: centralization (the antithesis of P2P).