On the Selected Text context menu (right-click on Windows/desktop), when you have random text selected, there is a menu entry “Search (searchEngine) for (selectedText)”. This is great. But when you have a valid URL selected, this entry is removed from the menu. I think this option should always be available, no matter what the selected text. This would be easy and make this user happy 
I do a lot of spam fighting for my organization, so I often want to see what a search engine has to say about a domain without actually sending the browser to that site (which often is a compromised one).