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.