The Web Shield is your primary defence against on-line malware/malicious sites, etc.
You only have to look at the old search results to see that not every entry had the Avast tick/check mark along side it (only those it knew about or had information).
Even those sites with that check mark would be scanned by the Web Shield when you try to connect.
The web shield was there way before the avast browser extension came into being.
Firefox, has a much smaller user base when you compare it with Chromium based browsers, so the workload to maintain this for Firefox, is exponentially greater than it is to support all of the chromium based browsers.
Both Firefox and Chromium based browsers have frequent browser updates, so the workload is high to maintain compatibility with the browsers and the Avast Browser Security app. Given the overhead isn't directly proportionate to the size of the browser user-base, something has to give.