I've been using the YN622C-TX and YN622C transceivers for about the last four years. I think I have gone through maybe three or four sets of alkaline batteries in the TX.
The transmitters and receivers don't use much energy at all. The transmitters are very low powered radios that only transmit a few milliseconds per exposure. The receivers are even more miserly in their power consumption. I do use the receivers much less frequently now that I have a couple of YN685 flashes with built-in receivers.
For the high drain flashes I use 2400mAh NiMH rechargeables. I've got enough NiMH rechargeables now that when the set that is in my YN622C-TX now dies I'll probably go to rechargeable batteries in it, too.
Like the instructions with most products from Yongnuo, sometimes the instructions lose a little in translation. I have a feeling someone misinterpreted the User Manuals that say they don't come supplied with AA size batteries (excluded) to be saying certain types of batteries are not to be used.
The User Manual that came with my YN-622C transceivers says:
Open the cover and install two AA batteries (excluded)¹ according to the + and - marks, rechargeable batteries of 1.2V can be used. Replace the batteries when the product does not work stably.
The User Manual for my YN622C-TX says:
Installing the 2 AA (1.5V) batteries (excluded).¹
There's no mention at all regarding NiMH or other types of rechargeable batteries.
The specifications in the user manual for the YN685 say:
Power Supply: 4xAA size batteries (Alkaline or Ni-MH battery)
¹ 'Excluded' here means the batteries are not supplied in the package with the transceivers. It does not mean the batteries listed are excluded from use!