Either way it is a public resource. On one side access to a countries fishing grounds to make money from it. On the other side access to a countries tax money to make money from it.
I get a feeling that you think fishermen should have some special heritage rights guaranteeing large profit margins rather than having to pay the public for the access to a shared resource.
If you introduce capitalism into the equation you are just opening the doors for the rich to exploit the workers in a systemic manner, and the workers in this case are fishermen.
Just do a standard fishing license you apply for and pay a nominal fee which can be refunded after some conditions are met, and then hand out quota evenly (or based on capabilities, history, etc.). Iceland already has a system similar to that called Strandveiðar for small fishing boats during a small window.
OR (and I like this better) ban trawling.