The 6502 had only the instruction pointer as 16 bit register, the 16 bit integers were handled with 8 bits with multiple statements, e.g. if you do in 16 bits c = a + b
clc ; clear carry bit
lda A_lo ; lower byte of A into accumulator
adc B_lo ; add lower byte of B to accumulator, put carry to carry bit
sta C_lo ; store the result to lower byte of C
lda A_hi ; higher byte of A into accumulator
adc B_hi ; add higher byte of B using carry bit
sta C_hi ; store the result to higher byte of C
8080 and Z80 CPUs at that time had 16 bit registers as well.
The Z80 CPU was still 8 bit architecture. It's 16 bit registers were eventually pairing two 8 bit registers, like BC, DE. The operations with them were much slower then with 8 bit registers because the CPU architecture was 8 bit, but this way 16 bit registers and 16 operations were provided.
8088 architecture was mixed, because it also had 8 bit data bus, but it had 16 bit registers, AX, BX, etc., lower and higher bytes also separately usably as 8 bit registers, AL, AH, etc.
So there were different solutions to use 16 bit integers but 8 bit is simply not a useful integer. That's why C and C++ used also 16 bit for int.