No, if you want your final output to be 16-bit (eg CD quality), then you need more bits to work with when mixing. Each operation you perform will be requantized

No, if you want your final output to be 16-bit (eg CD quality), then you need more bits to work with when mixing. Each operation you perform will be requantized (rounded) to 16-bit resolution adding a bit of noise each time, until eventually the lower 4 bits (for example) are nothing but noise, and your signal is effectively only 12 bits. One the other hand if you did that mixing at 24-bit resolution, then you still have 20 bits of good data remaining, you throw away the bottom 4, and have nice clean 16-bit data to distribute. 32-bit integer is overkill in most situations, which is why it wasn't implemented for so long. 32-bit float is used a lot because it has 24-bits of resolution, but also has a huge scaling range, so you don't have to worry about clipping during intermediate operations, just at the end.