I think we should be able to easily check profiles as websites, like steamrep.com/api/STEAMID responds "normal", "caution", "ban" etc.
It's easy like it is now. You just copy the user's profile link and paste it into SR and get all info which is needed. I don't see why that would be necessary.
He's talking about the API, not SR in general, hence this is in the API section. The API provides this functionality: http://forums.steamrep.com/threads/steamrep-web-api-beta4-legacy-public.114688/ Take a look at the response the API provides, under "summary" is exactly what you are asking for.
The API is NOT the search box on the home page, or any part of the UI for that matter, if that's what you mean. API = Application Programming Interface, this is the API here http://forums.steamrep.com/threads/steamrep-web-api-beta4-legacy-public.114688/ . This feature is already exposed through the "summary" item in the API. Not going to respond anymore in regards to this topic, since this is already in the API as much as its ever going to be.