This is one of the reasons I have said and posted that the manufacturers should offer the front end of AVRs along with separate power amps that handle the speaker load. If we were to count the threads here and on other forums, it's likely that the questions "Why does my AVR shut off?" and "Why does my AVR sound bad?" would be #1 and #2.
As you may remember, you sent a crossover design to me when I designed my speakers and again, thank you. Also, as you just posted, the impedance is in the 4 Ohm range, but that didn't seem to matter to the Denon AVR I was using- it never shut off and the sound from the system was actually very good. I replaced the Denon with Parasound equipment because I wanted to play my vinyl and, while the arguments raged about whether amplifiers sound different or if their power should be rated fully with all channels driven vs 2 or 3 , I noticed that this sounded better than the Denon and posted same. This amp has never shut down, run hot or had a single issue of any kind. OTOH, the spec sheet shows that it will handle 2 Ohms without problems. THAT'S what I want in an AVR, not "It's not as good, but it's OK" at the low, low price of $2500.
They could do this, but WAF is rampant and locating a power amp in a different location from the preamp isn't always easy/practical/possible. In the meantime, we have to pick our battles/choose our poison.