Can (CPU) logic and (flash) memory be located on the same die?
In answer to your question: YES. 

Read Microcontroller, and you might be pleasantly surprised. 

Microcontrollers (MCUs) combine logic (CPUs) with non-volatile Flash memory, RAM, and sometimes EEPROM or FRAM.

MCUs also have digital logic to implement peripheral interfaces, such as SPI, I2C, UART, Timers, USB, CAN, etc. MCUs usually include relatively large current drive capabilities, compared to the transistors internal to the circuitry, in General Purpose I/O which interfaces to the circuitry outside the chips package. 

MCU's sometimes contain analogue circuitry such as analogue to digital converters (ADC), operation amplifiers (OpAmps), analogue comparators, digital to analogue converters (DAC).

A more extreme example of integration is Radio. For example, Atmel, NXP, ST and TI all claim to manufacture single die Radio and MCUs.

Everything is on a single die. That is crucial because manufacturing costs would be higher otherwise. You can buy an MCU at under 0.5 GBP, one-off, and have a range of sub-$ device choices. 

The markets for MCUs are diverse and large. However they mostly have one thing in common, the MCU is 'embedded' inside a product. Bringing a mass-market product to market is typically slow and costly, and they are sold as complete, finished, products. 

Hence most people are unaware of MCUs, or the MCUs role in the modern products. (I have first-hand experience because I present talks and workshops to the general public, as well as education about exactly these topics.)

Visit a distributers web site, for example Digikey, Mouser, Farnell to get a sense of the range of products. Some of those examples claim to have over 10,000 different MCU parts.

Interestingly, the human race manufacture about 30-50 times more MCUs (devices which incorporate al of the pieces of functionality) than devices which don't (microprocessors).

I believe the MCU market is as bigger or bigger than the microprocessor market too, though I find it hard to get up-to-date numbers.

Some of the companies which make microcontrollers are listed in Types of Microcontroller though that list is incomplete.