There is
no problem charging flight batteries and RC at the same time, IMO. I've been doing that for over 2yrs on my whole fleet and no problem at all. The only downside is it slows down the charge rate of the batteries, which is OK if you aren't pressed for time. I do the same with the DJI 90W car charger, no problem.
If you recall the P3A had a 55 watt charger. I believe that statement about charging both at the same time was targeted at that 55W charger, but DJI never said that. And, I think the same verbiage got into the P3P manual by mistake, or ignorance, IMO. The P4 and
P4P does not have that verbiage in the manual because all P4 craft come with 100W chargers, implying it's OK to charge both at the same time, and I agree, it's OK. Nobody in this forum in 2+yrs has ever had a problem charging both at the same time to my knowledge, and that's a lot of people. I'm sure the OP's problem isn't attributed to charging them at the same time, evident because charging separately had the same results.
The dead flight battery issue is common, and the RC battery issue has been seen too, but that's usually the RC battery will only half charge. But having both of these problems at the same time with a new purchase is really odd, or simply really bad luck. I tend to believe it was charger related, but anything is possible. I think the OP did the right thing, sending it back to the vendor, that's what I would have done, it's just faster.
I've been harping for months about DJI's lack of outgoing test and visual inspection. It's obvious they don't have outgoing inspection or test. If they would add just one minute of basic visual inspection and test when they turn on the craft to link the RC, they would find lots of problems in their craft, allowing them to fix them before they get boxed. That would be a lot cheaper than dealing with all the returns they have today.
I had a bad gimbal in my
P4P upon receipt, and this could have easily been found if they simply LOOKED at the craft while it was on during the LINK PROCESS with everything is powered up. All they need to do is hold the craft while it's on (no props installed) and rotate the craft around, watch the gimbal stay level, and feel the gimbal base. Mine would vibrate when tilted left 20 degrees, it was easy to feel and reproduce, you could hear it too. After the craft is booted with no props installed, it took me 15 seconds to find the issue, but DJI doesn't bother. This vibration caused jello in the video when hovering in a wind from the left.
If DJI added ONE MINUTE of test and visual inspection to their process, they could also eliminate the very common CROOKED camera problem so many get. That problem is very apparent, it can be seen in less than 5 seconds during the link process, just LOOK at it and you can see it.
DJI would save themselves lots of money if they had outgoing inspections, verses the thousands of DOA (defective on arrival) returns they deal with. I don't understand why they don't realize the money they're throwing away due to a poor QA process.