About free SaaSS equivalents

[ilias.k.cs at freemail.gr]

Hello,

Can p2p technologies generally be thought of as free replacements for SaaS ; I'm thinking that one can, in theory, build a Google Docs p2p equivalent that is absolutely free.
As it would be peer based, not client-server then-informally speaking-everyone would have access to the same code (the only requirement being that you may connect only to peers that have the same version as you do).
Isn't this the way you can provide truly free alternatives just like you do with non-conventional software?
I'm asking that question because I haven't seen any campaigns for providing alternatives to SaaSS yet, and I wonder whether there is something wrong with my line of reasoning (too naive?) or I'm just not a good surfer (been a while since someone said surfer, lol)
And I know that one can run his own service and be free, but there are cases where having a service without anyone else to be served but yourself doesn't have much point.

Thanks,
Ilias K.