Only having one ADC can be an issue when you need readings to be in phase, but for reading any sort of human interface device it doesn't matter at all. Just cycle through your inputs one at a time. Some microcontrollers even have hardware to scan through multiple inputs automatically. You can use DMA to read the ADC and send data out over whatever communication peripherals your microcontroller has without using much CPU time.
If you are using USB HID, you are limited to a 1000 Hz update rate and that's really overkill already. You can have up to 8 analog axis in a USB HID game controller plus lots of buttons.