EEPROM is more expensive per bit than flash, so it's only used where it is needed. Sometimes the EEPROM is left out entirely, and applications that require EEPROM have to use an external chip or use some trickery to make flash pretend to be EEPROM. It doesn't make much sense to compromise 2048 Kbytes of flash for a few bytes of non-volatile memory.
If I recall correctly, there were a few early MCUs that had a small amount of EEPROM for program memory (and no flash), but they could not compete.
In most cases flash will only be programmed once or twice, and having to erase it in large blocks rather than byte-by-byte is not an issue, so the designers will use the least expensive memory that meets their high-volume end-user requirements.
The datasheet states 10,000 times minimum endurance for the flash on the ATmega328p, so that's enough for most practical situations, even development where it may be reprogrammed many times.
● Write/erase cycles: 10,000 flash/100,000 EEPROM
However, note that the data retention time may be reduced by many erase/write cycles, which is a reason for not shipping development units into the field. From the ATSAME70Q21 datasheet:
Earlier MCUs often used OTP (one-time programmable) EPROM (but with no physical window for the 'E' on production chips) for the program memory (and they may have had a bit of EEPROM).
There are a few MCUs that use a different technology for the program memory and can be reprogrammed more times- for example TI's Ferroelectric FRAM technology MCUs.
Market disadvantages of FeRAM are much lower storage densities than flash devices, storage capacity limitations and higher cost. Like DRAM, FeRAM's read process is destructive, necessitating a write-after-read architecture.
FRAM memory has a limited number of lifetime read cycles so even if the higher cost is okay, it's not a panacea.
There certainly disadvantages of flash- it's relatively slow compared to RAM, it's erased in large blocks, so a lot of information has to be re-written to change a single bit, limited number of write cycles, requirement for an on-chip charge pump etc. but the high density and low cost is what makes it the dominant technology.