It is true that independent workers don’t have a fixed schedule, but they are part of the economic environment and therefore are still affected by it.
Let’s say the independent worker decides to work long hours, 12 to 14 hours per day. As work-time reductions progresses, the supply of jobs will increase, and therefore, firms will be looking for more workers. A we have seen before, those positions will be supplied by many different sectors, but also, some of these entrepreneurs could decide to enter the labor market, after seeing that people can have decent income working only 6 or perhaps 4 hours if it the work-day is already at 4 hours a day by that time. The work/life balance will become attractive for some entrepreneurs who are working 12-14 day. Of course, others might decide to stay. At the end, it’s up to them.
With these dynamics, two things will happen. Some of these independent workers who entered the workforce were probably his/her competitors and now this entrepreneur who decided to stay independent has fewer competition in the market. His revenue might increase and he might have better possibilities to control the amount of time he spends at work. On the other hand the pressure from his/her spouse to spend more time at work, coupled with them being witness on how other friends, neighbors or relatives who have regular jobs can have a better work/life balance with their shorter hours, will make the entrepreneur consider cutting back on the hours spent working, either by making shorter hours work for his/her business or working for a firm with shorter hours.
This answer is of course speculative. The question demanded, however, some sort of speculation, since such scenario has never been reported before.