Would it not be wonderful to have a pay cap on the ratio between the highest paid employee and the lowest paid? We could extend this to all sectors.
I like the sentiment, and we shouldn't let fear of unintended consequences prevent all human progress, but there are significant risks with regard to unintended consequences and concentrating government powers on wages and social programs beginning to approach failed utopian experiments of the past.
As other commenters have skillfully pointed out, this would likely have deleterious effects unless, as you say, it was implemented in a fully-downstream fashion to include the whole pool of workers including contractors and the like.
And of course, when regulations get too stiff in one city or state or nation, companies move. That is also a big obstacle in this idea. But there is at least one company that has the CEO salary capped at a certain number of multiples of the lowest-paid employee, and their culture seems to be great.