I agree with you about the lawyers getting rich!
There was a case a little while ago where an asylum seeker was awarded what looked like a huge amount but on slightly closer inspection, it transpired that the lawyer got most of it as fees.
I do think that these lawyers-the equivalent of ambulance chasers-are a blight.
Here is how I would fix it.
I would eliminate-totally and absolutely-legal aid for asylum seekers and refugees.
The lawyer could of course take on a case if they chose, on the strict understanding that they would not be receiving one penny from the public purse for doing so.
I'm not Mystic Meg but I foresee that if this simple policy-no legal aid, no not even expenses-were followed there would be a sharp fall in asylum seekers managing to delay their removal from this country.