Why should the players not earn money? If they are selected in the leagues, they should be allowed to play there. Playing in leagues is much better than playing FC because in the leagues you get to rub shoulders with world-class coaches and players. Of course, they should not be allowed to play dodgy leagues like Qatar T10 but there is nothing wrong if they want to play in CPL or T10 League.
Before you compare them to Australian and English players, Centrally contracted players from those leagues earn enough for them to play no other league than IPL and even from IPL most of them earn near millions. First of all, its unfortunate that Pakistani players can't play in IPL from where they could have earned a lot of money and secondly they don't earn a lot of money from PCB and PSL too so they have every right to play in every league in which they are selected (except for the dodgy ones like Qatar T10).
Blocking players just because they are requesting you to give them NOC is a very cold behaviour. What's wrong in replying back to them. It's like my professor blocking me from email because I asked him for extension of CW in uni.
Then the players can reject the central contract and play leagues. PCB shouldn't be able to stop any players that make themselves unavailable for selection for the national team that are not centrally contracted. For example, Wahab/Nawaz/Tanvir are all playing in South Africa right now. I don't think PCB should be able to stop them unless they're centrally contracted.
But once you have a central contract then you have to understand that the PCB is your boss. They can set the terms of that contract and if those terms state 2 leagues maximum then you abide by it. That's how contracts work.
Secondly you really want Babar Azam to play in a UAE T10 league before a test series against Australia?
These players are assets of the PCB. Imagine, Shaheen Shah Afridi getting a stress fracture at a T10 tournament and missing cricket. PCB invests in these cricketers with academies, facilities, doctors, coaches, nutritionists etc year round.
And no it's not like you emailing your professor. It's like you whatsapping the dean of your university to register for a course (maybe one that requires prerequisites you haven't completed). How many of your professors do you whatsapp?
Also it's not cold behaviour if you set the terms out clearly in the central contracts which state how many leagues they can compete in and the proper protocol for obtaining NOC's. You can add that NOC's will not be withheld without just reason.
Let me reiterate, players can do as they please but if they are centrally contracted then the PCB is their boss. Do you think Liverpool would let Moh Salah go play 5 games in the Chinese league in the off season so he can maximize his earnings?