If a four-day workweek can be implemented without a loss of production, then profit-seeking capitalists will leap at the chance.
No, they won't, because that's not how capitalism works.
The capitalist will see their employees doing five days work in four on one side with shareholders screaming for ever higher profits on the other and will make a business decision to have their employees go back to working five days while producing six days worth of work for the same pay - they get the benefit of higher productivity and the profits from that, pleasing shareholders, while you just get more work.
Why does it need to be a goal of governments?
Capitalists will do everything they can to maximize profits to the exclusion of everything else and will fully expect you to do six days work in five for no change in pay. Governments, when they're working properly for their citizens, are supposed to be there to protect the people from being exploited like this.
They're supposed to setup rules telling companies who implement four day work weeks, finding employees can keep up with five days output in that time, should not only continue to be paid for the five days worth of effort they produce but when they have to work that fifth day then they will get paid the equivalent of the six days worth of production they're producing.
Capitalists won't do it on their own out of the goodness of their hearts, it goes against their fiduciary responsibility to maximize profits at all costs, so they have to be forced to do it by law so yeah, Government.