The exact number is 1112064 = 2^16 - 2048 + 16*2^16: in UTF-16, 2 bytes can encode 2^16 - 2048 code points, and 4 bytes can encode 16*2^16 (the 2048 surrogates are not counted because they can never appear by themselves, they're used purely for UTF-16 encoding).
Yes, that was exactly the reason. CJK unification happened during the few years when we were all trying to convince ourselves that 16 bits would be enough. By the time we acknowledged otherwise, it was too late.
The exact number is 1112064 = 2^16 - 2048 + 16*2^16: in UTF-16, 2 bytes can encode 2^16 - 2048 code points, and 4 bytes can encode 16*2^16 (the 2048 surrogates are not counted because they can never appear by themselves, they're used purely for UTF-16 encoding).