9-bits sufficient? Maybe not, there's 500 steps alone between tip extremes - min(350F) and max(850F). Someone else may want to comment on higher resolution and/or over-sampling to establish delta, but more data is preferable than less.
1) Discussion was about MCUs not having 17bit ADCs. I question this is needed. 10 or 12 bit ADC would do the job. Jelly bean MCUs have it.
2) It doesn't display to that resolution, so, yes, 9bit is fine. In fact, if it rounds to 5deg C, then even 8bit ADC would do the job (assuming ADC is only for display and control loop is analog).
3) No point in having more data if it is thrown away. Also, ADCs with a lot of resolution are harder to make them properly working. They easily pick up noise from environment, power rails, etc. Even 12bits is not easy to utilize (as stm32 demo boards show, I've seen noise up to 3 LSB).
Just in case, I'm not saying they are doing it wrong or something. I just like to discuss the design and learn something from it. There can be non-design reasons to make the station this way. May be they just had tons of these 17bit ADCs for free and decided to use them. Or they just wanted reduce design costs/time and put parts with overkill specs, who knows.
BTW how does AccuDrive works? Everyone says "wow, it is spot on", but I'd want to know details. Because may be Dave received a special calibrated unit with pre-selected tips.
PS any hi-res photos of the PCB available? Want to see how active rectification works... I have two ideas how it can work (e.g., using comparators to switch mosfets, or a self-driving circuit if load is resistive).