Is there a way to search for the past day's or week's posts without entering a keyword?

Or was that a deliberate decision not to allow that so as not to result in some overheated threads?

Yes. On the search page, there is a box that says “show messages” Click on that box and you have the option of posts within the last 24 hours, within 1 week, a month, 2 months, 3 6 or 12 months. You can also select a specific date.