Put all search results on a single page (with facets?)

Something that has long bothered me about core search is the fact that each search implementation provides a separate page. The pages search/node search/user always bothered me, especially the fact that the navigation pattern on these pages is those dreaded TABS.

I would love to see all the search results aggregated together onto the main /search page, with filters (facets!) for search result type. Lets get rid of the "Default" search, and those tabs!

A thought: Is this something we can solve easily by turning the search-results page into a view, with exposed filters?