Are there any flash micros today that can't write their own flash?
Depends what you mean by "write their own flash". Quite a few MCUs require an external high voltage, as the die area needed for a charge pump has been saved. Many require a complex protocol on the JTAG port, with fairly precise timing, in order to program the flash. Many which can do their own programming just by being supplied with the necessary data require software loaded into them to be able to do this - e.g. a JTAG port is used to load the programming code into RAM, or an initial JTAG controlled programming sequence gets the programming code into one segment of flash, from which the other segments of flash can be programmed just by feeding the MCU the data.
You might expect savings to only be made on small devices, but some big complex automotive MCUs lack the internal charge pump. This might possibly be a safety issue - ensuring the code can never change accidentally in the field, if the MCU gets kicked into an unfortunate mode. This is a common cause of corrupt flash MCUs when complete internal control of the flash is provided. Quite a few projects need their code updated for this kind of problem, when returns from the field flood in.
When you look at things like FRAM density versus flash density, the high voltage charge pump is a big factor. Its a large overhead when the flash is small, but a small overhead when the flash is large. This is why you see things like TI focusing its FRAM efforts on smaller MCUs.