There are constitutional and legal subtleties here that need to be understood before we rush off and abolish the G-G's position. For starters, read
this carefully.
It ought to be clear from the first page of that link that the G-G does have a legitimate role under certain circumstances, and not merely those involving natives. They seldom arise, but when they do the G-G's presence can be crucial, as in the King/Byng affair. There's no doubt that in a legal and constitutional sense Viscount Byng did the right thing there, and generations of scholars, including the redoubtable Eugene Forsey who wrote the stuff at that link, have agreed.
The Queen is formally the Head of State, the Prime Minister is head of our Executive Branch. The U.S. President has both roles; that adds a fairly onerous list of ceremonial duties to his executive ones, which he could certainly do without. That in itself I think justifies two positions. The French have separated them, they have a President and a Prime Minister. There's no reason we coudn't do the same, just rename the office of G-G to President and leave everything else as it is. It could also be argued that in a system like ours in which a government can in principle fall at any time, it's necessary to provide continuity between governments, which is the essential role of the G-G and what the King/Byng affair most clearly demonstrates.
For instance, if Paul Martin's government falls, the G-G would be within her powers to ask Stephen Harper to try to form a government, on the assumption that he could work out some kind of coalition among enough MPs to meet the House and survive non-confidence motions. Not likely, but the point is that she could do that.
And I think somebody has to be able to do that, because of the constitutional and legal definitions of how responsible government works in the country. Abolishing the G-G's position has far-reaching implications that would require many other profound modifications to our current system, with completely unpredictable results. So the question has to be asked, what problem would it solve? If there isn't one that's far more serious than the cascade of changes it would produce, why bother?