Solution is ok if you have enough pins left to be used.
If you are running out of pins another solution would be to mount an I2C backpack onto the lcd display. I2C needs only 2 wires (SCA and SCK) which use pins A4 and A5 on an UNO/Nano.
Each I2C device comes with its own unique address, so you can hook a lot of more I2C devices in parallel, using only 2 dedicated I/O pins in total.