The premise that all AVRs sound the same, or that the differences are vanishingly small is a bit too generalized to be accurate. There are several reasons an expensive AVR could sound better than a cheap one. Here are some of them.
Power output. It’s not just the rated power per channel, it’s the rated power, dynamic headroom (the ability to handle peaks above the rated power) and the ability to drive multiple channels at the high dynamic peak level simultaneously. The most expensive single section of an AVR is the power supply. An inexpensive 7.1 channel AVR (8 channels), rated at 100W/channel is incapable of producing 100W from all channels at once. That would require an 800W power supply, minimum, and they don’t put those in cheap AVRs. The cost of such a power supply might easily exceed the total cost of some of those receivers. As the price of receivers goes up, one thing that improves is the power supply. Even $2000 AVRs sometimes can’t deliver full rated power to all channels simultaneously, but the better and more expensive the power supply, the closer to it they get, and can do so in at least the front 3 channels. It’s rare that a film soundtrack would require that ability in all 8 channels, especially if you have efficient speakers, or play at low volumes, but with less efficient speakers in a larger room, and playing sound at ‘reference levels’, the ability to drive all channels with full power becomes an issue.
Using the preamp outs and separate power amps can accomplish this goal. Any two channel power amps of decent quality is capable of delivering full power to both channels simultaneously, so using 4 external power amps results is higher simultaneous peak capability.
As a point of reference, THX Ultra2 Certified receivers are tested with all channels driven, and you won’t find one with less than 100W per channel, typically more like 130. THX Ultra2 is a certification that includes all audio components in a room of up to 3000cu ft. By contrast, THX Select2 receivers are power tested with only one channel driven at a time, and must meet lower peak current ratings. Select2 products are intended for rooms up to 2000cu ft, and are meant to be more affordable.
Could you hear the difference between an Ultra2 and a Select2 receiver? That depends on the size of your room and your speaker efficiency, but if played to THX reference levels, the answer is yes. More importantly, could you hear the difference between a THX Certified product and one that isn’t? Remember, it costs real money to design, develop and certify a THX product, money you wouldn’t have to spend otherwise on a similar product. Again, the answer is “yes”, and that would be not only for reasons of good and certifiable design, but also for reasons of THX processing in the line level stages.
Another power-amp factor, which is usually not specified, is output impedance, which directly relates to the amp’s ability to drive a complex load such as a multi-driver speaker. Low cost amps may have higher output impedance, and if the speaker’s load impedance is complex (most are), they will sound different than if driven by a higher cost, lower output Z amp stage. The relationship is not strictly cost, but in general, lowering output Z increases unit cost. Damping factor is directly related. Higher damping factor results in more ability of the amp to control the speaker, a generally desirable trait.
The line level stage in a receiver has little to no audible effect, and that includes the DACs. With the exception of exotic over-sampling techniques, noise shaping, etc., the fundamental limit to performance is the digital word length and sampling frequency. At 24 bits, a digital system is about at the limits of what can be done in the analog domain, in terms of noise and distortion, but at 16 bits, analog circuitry can easily surpass the performance of the digital system. By the way, noise is not a subjective quality. It is clearly audible, and the audibility of noise is well known. The audibility of harmonic distortion is also well known, but the threshold of audibility is not widely known to consumers. We are used to seeing audio devices with distortion figures in the .01% range, yet the typical listener only begins to hear odd-order harmonic distortion well above 1%, and that depends on the signal type. Even-order harmonic distortion remains inaudible up to 10%! Inter-modulation distortion (IMD) is perhaps more obvious that THD, but then it still has to be in the single whole-number digits to be heard, and is also signal dependant. Given all those figures of the threshold of audibility of distortion, no receiver should have distortion that would affect the sound subjectively. And you can include TIM in that too, it just shouldn’t be a problem.
This reduces the possible audible differences in receivers to three areas. First, the power supply’s ability to supply power to all channels under high demand, second, the amplifier’s ability to interface with a complex speaker load, and third, DSP functions in the line stage, like special processing, EQ, Audyssey, THX processing, and so on. Those functions depend on DSP programming, which is not at all fixed or even similar brand to brand, beyond standardized functions like Codecs and ProLogic, etc., and are all DSP functions are likely to be audible, most by design. DSP firmware of higher sophistication is more expensive to produce, and could potentially raise the price of an AVR. And, personal preference for certain DSP functions could drive a receiver choice.
So I surmise that you can get audible benefits from more expensive AVRs. Cost justification is the subjective part. For me, I hate to replace audio gear. I own my audio stuff for at least a decade at a time, barring radical changes in function (like the advent of 5.1, for example). I like my stuff to be built well, and to be as reliable as a wood-burning stove. That saves me money in the long run, but costs me money in the short-term. Sort of like buying a Toyota over a Ford. Sure it costs more, but if it lasts twice as long, it’s actually cheaper.