I guess the problem is when you want to quickly provide a favicon with the search result (beit in the omnibar or actual search page), as you're typing and results are being displayed you cannot send off a request to the site, wait for HTML html to finish up downloading, send off a request to the manifest if its defined for multiple sites at once.
On a technical level of course its doable but in reality it's a complete waste of data and processing, not to mention it could take a long time to show up. I imagine they have these favicons all cached on their side so they can quickly send the right file down and/or do this processing if needed.
That being said maybe they should just not use a favicon if it's that big of a deal.