You can't run anything on an RP2040. There's no Flash or code space.
RP2040 sits at an awkward placement. It requires external parts, but low end SPI parts and not the nicer proper RAM like DDR3L or the like.
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My point is that if you have a design that fundamentally requires external parts like the RP2040, the accurate comparison is against MPUs. Chips that are specifically designed to work with powerful and cost effective external components.
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Analog-focused designs like ATMega, ESP32 or STM32 comfortably do things that the real computers or MPUs cannot do. Like read a voltage, work with OpAMPs or other analog stuff that cannot fit on a proper Linux computer chip like SAM9x60D1G. And to do so without any external parts, so that you have the simplest design possible.
Glad you mentioned Microchip. The PIC32MK family is MIPS architecture microcontroller, with hardware floating point unit, running at 120 MHz, with a whole slew of peripherals, like 10 MHz unity-gain op-amp, D/A converter, lots of flexibility in mapping peripherals to pins, fast A/D, DMA, etc..
ESP32 chips also need external SPI Flash, and many STM32 have little flash and QuadSPI with execute from external flash capabilities, so I don't see this as a specificity of RP2040.
Turns out you can actually run quite a lot with dual core CPU clocked at 250MHz. You can also use part of the flash as file system, but that's not quite as straight forward.
