Just playing the devil's advocate here, but would you not say Google's search homepage has a lot of "wasted space"?
I don't think one can always make such a quick judgment about whether space is a bad thing or not.
I would not say that, no. Google's search homepage does not have a primary function that is similar in any way to Gmail's primary function.
The Gmail homepage, of course, should be showing you as much data as possible; as many emails as possible with enough contextual data and UI to read/delete/sort them.
Google's search homepage isn't an information-dense medium.
It's a fucking search dialog. It should be clear and simple.
Now: the search results pages should be informationally dense. And for the most part are (though I'm finding recent changes to be net negative).
Note that search engines which have gone in the direction of packing a shit-ton of distractions onto their homepages in a desperate move to chase "monitization" lose out -- look at Yahoo and Aol, virtually clones of one another at this point, as well as synonyms for Internet failure.
The Gmail homepage, of course, should be showing you as much data as possible; as many emails as possible with enough contextual data and UI to read/delete/sort them.