Profit isn't exactly the problem here. We could pay people to fix various kinds of infrastructure, they could make big profits, that would be great - if only they existed and had figured out their business plans.
If we're not going to allow that, there's no need for money at all. We'd vote on what needs doing, and it would always be something like mending roads, and we'd all have to knuckle down and do it, through a conscription-like system, on pain of pain. It would never be fixing the broadband, though, because broadband is a crazy imaginative project, like building a pyramid, so there wouldn't be any.