ARM chips that lack boot ROMs
My question is this: do there exists ARM chips that lack any sort of boot ROM


Yes. The Atmel/Microchip SAMD21 series operates this way, for instance -- there is no embedded bootloader; if the chip is fully erased, it won't do anything.

I wouldn't be so quick to treat these parts as being fundamentally different from others like the STM32, though. The BOOT pins on the STM32 control the reset address -- if the part is set to boot from flash, the embedded bootloader is not involved in the boot process.