That 10k to ground absolutely should NOT be there. No way. Those pots need an absolutely stable voltage to be putting out a valid level. They are designed to output a ratio of the power source - i.e. +V to GND. I've connected up to 32 pots in a similar circuit, and they work fine. They were all 10K pots. If you have a problem with the total current draw, then you need a higher current power source. If you are worried that the pots will overheat from the individual current in each pot, you need a lower voltage. And if that lower voltage is not enough to get a valid reading from the ADC, then you will need to individually amplify/buffer each pot. But I doubt any of that is necessary with typical devices. Just loose the 10K and you'll be fine.