Because the point of a HIAC, from the beginning was supposed to be "You can't escape" or you can't get away from your opponent. Not, I'm gonna put you through the top.
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the original purpose was that shawn kept running away and cheating...thus the cage.
there's been no "im running away" from HHH or Tista..
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True, but it's also been billed as 'most dangerous match' ever. Every time there's been a HIAC I believe someone's been 'injured'. Even if it was just that, really bandage up soar, injured. And more specifically every time HHH has been in there, and it's always been his opponent. So common sense says HHH would want to challenge Batista in a HIAC to do away with him once and for all, based on past experiences. And that is, that HHH's opponents always come out hurt, so HHH thinks there's no way Batista can win...
So it just goes back to the 'his match' logic, which in this case...actually works.