The main culprit for all AVRS is, that all built-in amps are using a single unstabelized power supply (transformer), which hamper the available current the more channels are used at the same time. From the physical size and weight there are limits to this, so this seems to be an invisible wall they are running against. Class D might push this somwhat upwards, but the "solution" would be a preprocessor + external amps, which increases the space constraints again unfortunatelly...
The root cause limit is a 15 amp 115 volt power outlet.
The second, and typically more important in AVRs, is cooling.
Most gaming computers use liquid cooling with low noise fans and huge heat sinks.
But stuffing 11x that in an AVR would make it too big.
One thing to remember, particularly if you use the bi-amp feature, is that the power requirements to achieve a given volume have a largely inverse exponential curve with frequency.
So you can largely discount the "high" channels in terms of overall power.
Using one or more active subwoofers will also greatly reduce stress on the AVR power supply. Particularly if you set the crossover to the THX recommended 80hz.
But you are going to have to hire a good electrician to rewire your listening room because most homes don't have multiple 15 or, better, 20 amp branch circuits in the same room.
So plugging your AVR and sub(s) into the same branch circuit will not help much.
The superior solution remains a good processor and one or two good multichannel amps designed to handle nominal 4 ohm loads. Along with two good powered subs properly located.
You still need to have the room wired to provide 15 amps to each sub, 15 or 20 amps to the AVR and another 15 for peripherals.
And don't crowd ventilation by using small or closed cabinets.