it’s completely possible. whether you think it’s worthwhile is another matter; it will be relatively expensive (mcu with USB host, sixteen channels of DAC, four four-channel VCA chips, the cost of your time to write all that damn firmware).
sixteen analog jacks into a CLUMP or derivative is much less hassle. keeping things in the analog domain means you can just use the 5V CV outs on the 16n, you don’t need any firmware or MCUs or USB hosting. just power to the mixer, and sixteen control lines.
also, as mentioned elsewhere, the I2C jack is probably a better fit, costwise, than USB; simpler protocol, highly suitable for this, but you still need DACs. There may be ways to do something clever with fewer channels of DAC and hold-capacitors, but that’s an exercise for the reader.