It depends what you're searching for. And searching within a range yielding lots of unsorted results is often unhelpful too. Of course, you can get around this with the API, but that is a lot of extra work for a student or non-computational researcher if they don't happen to already have those skills.
You can already do that on Google -- press "Tools", then use the dropdown to change "Any Time" to "Past Week", or use the Custom Range option to select whatever time period you want.
The question is whether you should also be able to do a strict order by date, without regard to ranking. I'm not sure if you'd ever really want that.
Yes, I use the filtering tool all the time. As a use case, consider where you're trying to find information about an incident or criminal case, where you can specify your search quite narrowly. But although news reports generally have the publication date extracted (and highlighted) as metadata by Google, There's no way to sort on this. It's a huge pain in the ass from a research perspective, because reports of crimes and arrests usually get far less coverage than reports of sentences or appeals, so the top results tend to more sensational but less informative.