I recently worked for a Belgium startup in the NY office. Many of my coworkers in the old world had an agreement to work less for less pay. When I asked my HR in US to reduce hours for less pay due to Covid-19 the answer was exactly like OP listed: "we have always done it this way... it's not possible in US ... if you decrease your hours by one hour you will count as half-time employee and lose all benefits".
In an instant I would give up 20% pay for an extra day off. Covid-19 is far from over and lots of parents are still juggling all sorts of issues.