This statement amazes me. It may be true, but it is very counterintuitive to my experience.
A micro USB connector is about $0.35/unit (for quantites of 1500). An HDMI connector is about $0.50/unit (similar quantites). These prices are from Digikey. So, in larger quantites from larger distributors, you could certainly get cheaper prices. The cheapest ARM processor (cortex M0) is about $0.78/unit on Digikey. I understand your point is about licensing the ARM design and integrating it into your silicon, but most low cost devices I've seen have just been PCBs that integrate these off the shelf components. I would have to imagine the cost of hiring engineers to do the VLSI design/integration, the cost of licensing the ARM CPU, and then the cost of fabricating/testing your silicon would have to exceed integration on a PCB. So, I would then assume that the processor, while certainly cheap, is still a very substantial portion of the cost of the device. But, I have no data on the cost of ARM licenses to back that up. You're definitely right in asserting the trend is cheaper and cheaper processors, but I don't think we've arrived at the "processors are so cheap they're basically free" world quite yet.