Hold on, I thought you were advising mixing in 16 bit? Have I misunderstood?
I'm not advocating mixing in 16-bit. I'm advocating not keeping your signals too hot for a downmix and master to a 16-bit listening format (e.g. Compact Disc).
Mixing in a higher resolution is essential, as is recording in a higher resolution... but do so while keeping the limitations of the final format in mind. e.g. You'll still want to implement a 20kHz lowpass filter for anti-aliasing. You'll still want to avoid recording signals so hot that their amplitude values exceed the dynamic range of 16-bit, even if you're recording in 24-bit.
But by all means record at 24-bit and mix in 32-bit floating to take advantage of high resolution DSP effects.