From a philosophical point of view this is extremely important. For example email used to be properly distributed. Nowadays the internet services are concentrated. For example gmail receives a big share of all emails. Amazon gets a big share of all http traffic, and so on.
In this centralised world the "client can be a server" attitude is in practice less important. NAT's are ubiquitous. Last-mile carriers don't give static IP addresses, etc.
But still, I would be much happier if the internet was truly decentralized. Even if it's not possible to decentralize all services, the internet, the addressing scheme and infrastructure just _must_ be symmetrical. Everyone connected to the net should be able to "publish" content without the need for anyones approval or infrastructure.
IPv6 addressing scheme, the removal of NAT's, brings back the democratization of the internet.