ANY hobby starts to get expensive as the years pile on.
Golf is one example, but try model airplane flying, go-cart/auto racing or AutoX (my personal non-AH hobby), boating/fishing, hunting, gun collecting/shooting, home theater, and you'll find that they're all MUCH more expensive than your Aces High habit.
And at least the computer upgrades get used for other things. Ask your wife how she'd like to browse Ebay (or whatever) on an unupgraded 6-year old machine. She'd want to shoot herself.
You were always going to get new computers every few years; AH just made you spend slightly more on video cards each time.
Tell your wife to do the math for some other hobby, and then remind her that AH keeps you in the house and out of trouble with the boys elsewhere. She'll come around.
-Llama