There are a lot of possible ways to approach this, such as overlay networks where peers interested in a topic can learn of and publish updates quickly to others (e.g. pubsub).
IPFS needs not be a kitchen sink: it's very easy to layer entirely application-layer overlay networks that do other useful things.
The only way we are able to productively use git is because there is a convention to have some state in a non content-addressable location (.git/refs, .git/HEAD, etc...).
Saying that IPFS could replace the web means either: 1) Introducing shared mutable state; or 2) full knowledge of everything on the network.
I'm guessing that the existing web is what provides that layer right now. Is there any work going on for novel IPFS-based content discovery mechanisms?
Another thought: Given the content-addressable, immutable nature of this graph, how does one discover that a new version of something is available without a central authority? How could we discover the tip of a blockchain with IPFS alone?