I work with (consumer) internet gateways and the like. In Broadcom's SoCs the main chip is ARM. They have been moving away from MIPS for a number of years.

I'm less familiar with other vendors but I briefly worked with a Qualcomm-based device a few years ago and that was also ARM.

There might be some dedicated cores in those SoCs or devices for e.g. accelerators or Wi-Fi handling. I've seen ARC there but I have the feeling these are also moving to ARM.

I think that was only true a few years ago. Everything now, from router, NAS to other appliance are moving towards ARM.

MIPS and PPC are still being used only because of cost ( vendors selling other chips ). The replacement cycles is very very slow, but the trend is pretty clear.

The answer is: it depends.

Some are ARM, some MIPS, some SH, some even are PPC.

I guess the availability of Android is making a lot of "dumb appliances" run on ARM even if they don't need a screen.

But for basic dumb appliances, PIC, MSP, Atmel processors (either the old 8051 or newer archs)

Could be, but I've been shocked by some of the products I've seen that have a full blown ARM in them these days. My friend bought a mouse with a full 32 ARM MCU in it.