You could do it with many micro's ARM, PIC... 8, 16 or 32bit.... But the bigger / faster processors will give far better usabiliy... If you use a 100 pin 8 bit and a decent LCD driver, the results on a 7" will always be too slow... If you use a 32bit running at 100Mhz +... Well!! No contest....
I use a PIC32 and a 16bit LCD interface and the results are good on a 4.3" screen....