High Level Assumptions
I think your "typical viewing" is over stated. First you have to have households with more than three TVs, then of those households that have two or more kids of different age groups, and of those households that have kids of both sexes.
Not that there aren't homes that fit the scenario, but as a percentage of ALL households out there it is pretty small. Dish may well have looked at production costs vs households likely to need over three tuners would be needed and decided two 813s is an acceptable solution over having all installations get a 5 tuner box. Don't forget a hopper/joey combo is likely less expensive for Dish than a 722/211 or even a 612/211 combo. Even more so when factoring in install costs.
UVerse has been successful and they max out at 3HD/1SD streams with no option to go beyond.
I am also assuming Dish, it there typical way, will NOT allow more than One Hopper to be leased, you will have to buy the 2nd one at a very large cost (guessing over $600 like in the past)
Not sure that is a good assumption. I'm assuming a Joey will be priced at $7 the same as a 211. 1st Hopper will probably be "included" as the primary receiver. DVR fee will probably be $10 (like the 922) vs the current $6. (This is all 100% conjecture.)
Production costs for the 813 are probably not much different than a 722. They just need to find a balance in the fees to discourage folks getting two Hoppers for the hell of it and not running off too many accounts that need it. If they can get an extra $10 or so month for a second one, then it is a pretty good deal for Dish. I can see it being tied to a minimum number of TVs as well - two 813s for two TVs might not qualify, but four or five TVs with the supporting Joey fees would.
D* and the HR34 should help keep things in line.
I think I said somewhere else that I don't think the 813 will be the of the line. An "815" would be a relative minor, incremental next model IF they have a stable 813.