It is just one of the false promises of the brexiteers that stopping European migration will somehow make the immigration system fairer. I don't think it will, if based on quotas. Once the quota is reached that's it, no matter how good or important for the country the applicant might be.
Plus we have a system now, where if you are non European you can get a visa to work here if you meet the criteria anyway. All that will happen is that will extend to everyone. Meaning far more bureaucracy.
The disadvantage of what we will move to is that it does not give any special rights to our own citizens. In tthe current system, not only can we accept migrants from outside the EU but in addition any UK citizen can work in any member state of the European Union. That will be lost.
If we think that somehow there is burning desire among brexiteers to even out the immigrants between EU and non EU, how come some of the major campaigning themes around voting to leave were the fears that Turkey would join the EU or that Britain would be flooded with refugees? They have bought racism right to the heart of the debate. This idea that brexit will mean a fairer immigration system is disingenuous.