No, I have only worked in the legal profession for 20 years.
I assume you are referring to the practice of an automatic appeal in cases that receive a death penalty sentence.....
News for you.....you can also appeal cases in which the punishment is life in prison.....its just not required by most state law as in a death penalty case.
But as to your allegation, an appeal isnt exactly having a 'whole separate trial' as you put it.....the appeal process is there to review all aspects of the original trial to see if anything was done out of order or if the process was flawed in some manner and the accuseds rights were not properly considered. If found that the original trial was done correctly via the law and there are no outstanding discrepancies, the appeal hearing is largely a formality....not 'a whole separate trial'.