Armagh star Steven McDonnell feels the GAA should scrap the qualifers because the so-called 'back door' system is unfair to provincial champions.
McDonnell wants to revert to the four provincial title winners playing in the All-Ireland semi-finals.
"Without the back door system we would have been more successful over the last 10 years," the Orchard County legend said in an Irish News interview.
"The system in place has definitely cost us a couple of All-Irelands."
Of the four counties through to the 2008 Championship, only Cork are provincial champions.
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Kerry, who were beaten in the Munster final, are odds-on favourites to win the Sam Maguire trophy for a third successive year.
Next in the betting are Tyrone who did not even make the Ulster semi-finals after losing to Down.
"It is likely that you will have two teams in the final that came through the back door," added McDonnell.
"I would like to see the back door system done away with altogether.
"The Championship should be knock-out. There is a flaw in the system somewhere and it is somethnig the GAA has to look at."
The qualifiers have been in operation in football and hurling since 2001.
This year, Armagh won the Ulster Championship for the seventh time in 10 years but were then knocked out in the All-Ireland quarter-finals by Wexford.
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