Germanshepherdsmum
The public sector is there to serve the public - a four day working week might benefit the employees but it would not benefit the public.
Not all public sector employees are public-facing. There is much flexibility about when (and where) work is actually done, although I think there could be resentment if some employees were able to work four days and others not.
Even in public-facing roles, a four day week could lead to organisations being open for longer hours. For example, if somebody works 5 x 7/8 hours a week, they could work 4 x 9/10 hours. A bit of creative thinking could mean that offices are open longer, which would suit people who can't access public services during the normal working day.