Pixel size doesn't matter for low light performance. Total sensor area and quantum efficiency matter. It doesn't matter how finely you divide the light your receiving and converting into free charge. If you increase the amount of light your receiving (more total sensor area) and increase the rate of incident photon strikes to electron conversions, then you have better high ISO performance. It wouldn't matter if you had 10mp, 50mp, 120mp, or 500mp.
I get this, but I've wondered whether there might be some truth to the myth, though not in the way many people imagine. While I accept that your explanation is true, it applies when using identical tech throughout the sensor. I've wondered whether it's disproportionately more expensive to make high-density sensors and whether some compromises would be made to keep the costs of the higher MP sensors within reason. The practical result would be that higher MP had worse low-light performance, but only because it's not identical sensor tech.
There has certainly been a LOT of research into making smaller sensors (which pretty much always have smaller pixels) more sensitive to light. That research undoubtedly has cost billions. That said, most of the research into making better small pixels has been done to make ultra tiny sensors viable...the kinds of 1/3" down to around 1/8" sized sensors found in small compact cameras, tablets, phablets, phones, and every other device that uses a microscopic sensor. Each of those sensors is usually a tiny fraction of the cost of one APS-C or FF sensor, though, despite having considerably smaller pixels (between 1 to 2 microns these days, with a new generation of sub-micron pixel sensors coming very soon.)
You've written about all that before and, again, I don't disagree with any of it. I may not have made my point very clearly: I'm not talking about R&D, but about actual production costs. I presume that P&S sensors can tolerate a higher pixel defect rate than SLR-quality sensors, so yield is pretty high for those sensors. I assume
that keeping the defect rate down in order to get a reasonable yield is easier (hence cheaper) with recent, but not leading edge, technology. It's my non-expert understanding that there are many refinements that occur to get a beautiful new design to produce a high yield. I'm assuming
that this problem is increased for smaller pitch pixels and the needed smaller circuitry. Of course, once you get those production problems worked out the yield is comparable.