Alternatively, you get get a really nice preamp & amps and spend a lot
less than a flagship receiver. The new top of the line Denon, for instance, is about $6,000.

There are many pre-amp/amp/monoblock amp rigs you could get for significantly less than that.
It depends on why you want an integrated AV amp. Do you simply feel you could save $ by not having the tuner? If that's the goal, be advised that you'll spend more by trying it. The audio industry will charge you more for less- it's like skim milk. They take the cream out of the milk, yet charge you more for it.

At any rate, it boils down to economy of scale. If Sony (for instance) can sell 250,000 units of a particular model, then they can tool up & crank them out cheaply. If they sell 1,500 special models without a tuner, they must spend more money to set up a special assembly line, deal with stocking & distribution, etc. Not to mention it's one more item a retailer will have to distribute. At some point you get to where the "high end" stuff is, where stuff is handmade inefficiently in small numbers, with the cost of lack of efficiency passed on to the end user.
If you are searching for such a device to simplify operation, then perhaps a multichannel preamp would be just the ticket. Something like the Marguiles Daleth or the Adire Vaza might work for you. Add a DVD player with a DTS/DD decoder, along with whatever amps you desire, and you're set. Either preamp would run you about $1200, plus the cost of an amp. You could buy a pretty nice 5 channel amp (Sunfire, ATI, etc) and still be around 1/2 the cost of a top flagship receiver. You'd lose some processing power & flexibility, but you'd still have good sound and simplified operation.