- Google tailors results to users, so it shouldn't be considered a common carrier
- Google doesn't charge users for access, so it shouldn't be considered a common carrier
- Internet search isn't a vital public service, so Google shouldn't be considered a common carrier
I totally believe you that there may be reasons not to consider common carrier a magic solution, but... I disagree with all three of those points.
(in other words: I think two people searching for the same terms at the same time should see the same results, and I don't think it matters that the service is funded based on indirect (advertising / tax) revenue, and I do think that many people -- in all kinds of environments -- can reasonably expect Internet access and web search to the point where we should consider it a public necessity)