I think the crocodile tears about Cheney 2008 lie outside reality. The problem is, I don't see the Vice President carrying any state that has more than 8 electoral votes (assuming he is not running against Hillary).
Second, George H.W. Bush and John Quincy Adams stand alone among Vice Presidents for a reason. Both followed strong, popular presidents and most Presidencies, after 8 years, have more baggage than a sitting VP can overcome.
Lastly, it would have been political suicide for the President to dump the Vice President in 2004. The Vice President, of course, could have orchestrated his own retirement, but the tenor of the times and his personal dedication to public service outweighed any petty political considerations four years hence.
In sum, we are where we are because history inexorably delivered us here. Let the best candidate emerge.
I count 3 standing VP's that won: Adams (the elder), Van Buren, and Bush (the elder). Jefferson was a standing VP that won, but he was of a different party than his P and successfully challenged him. Your point is the same.
For what it's worth, American political parties have a somewhat better record of retaining the presidency if they run someone other than the standing VP, provided that the standing P has chosen not to run or is ineligible.
Of course it hasn't happened since 1952, and in that year, the presidency flipped anyway.