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1000 gold for 20 health and what is usually 160 dps in team fights is hardly "a bad deal".
Rarely do players bunch up so often that you'll get that 160 DPS for longer than a couple seconds at a time. Also, Sunfire Cape is subject to reduction from MR and so it's not exactly 40 damage per second. For around 1000 gold, you could have an extra HoG, almost a Giant's Belt, a Negatron Cloak + Ruby, etc.
And I'm confused how you see little use in them vs mage teams. Amumu's Despair is weak vs mages because it is % based not raw damage. Sunfire is the opposite, and with Bandage Toss and CotSM you can easily be next to that spellcaster. Combining Despair and Sunfire gives Amumu strong viability against the entire enemy team, regardless of composition.
What happens when the mages on the other team grow brains and use at least one Rod of Ages? 40 damage per second isn't all that great against a 2.5k hp mage. If you're so dangerous, the mage can easily shrug off that 40ish DPS and nuke the **** out of you. With a Sunfire Cape build, you're not likely to have much MR if any at all, so you're not going to survive as many battles.
I don't like Aegis on Amumu. Why? Until he's spamming Despair or stacking Sunfire Capes, he isn't a good pusher at all. Sure it's good for the team fights, but put it on a champion that can also use it to push a lane.
You really only need Catalyst and the occasional golem to fulfill all of Amumu's Tantrum spamming needs later game. Tantrum is more than enough to clear a mob lane; Sunfire is overkill.