So then the attacker could just intercept the request and save the cookie plus sequence number plus digest, and send their own request with the same metadata. So rewrite a few dozen requests from one page view to do whatever you want and eat the response. The user sees it as the page timing out, so they figure the site is being slow and hit refresh, which gets them the authentic page. Yeah, it'd stop Firesheep, but it wouldn't do anything to stop a real attack.
To avoid this, you'd have to MAC the whole contents of the request. But HTTP proxies tend to rewrite the contents of non-secure requests, so your MACs will break and stuff will fail randomly. The only way around it is, yep, encrypt the request. Integrity without encryption fails if you have proxies that expect to be able to meddle with requests.
There are admittedly some practical reasons not to use TLS for everything right now, but they're not prohibitive -- look at Gmail or typical bank websites -- and they're diminishing with time.