I agree with the original premise of the thread: the BMW shifter does not fit well with the overall ethos of the Grenadier, nor does it fit well visually in the cabin.
I think the ethos of the Grenadier calls for a manual transmission, but I'm not going to grind that axe. It is pointless, and non-productive.
However, I still think Ineos could have done better than the BMW shifter, and provided a shifter that is more mechanical and less electronic. Yes, yes, I know that even the "more mechanical" automatic shifters use electronics, but there is a difference between a BMW shifter and some of the other auto shifters on the market. Take the Jeep JL Wrangler shifter as an example of a "more mechanical" shifter: both the Grenadier and the Jeep use the ZF 8-speed automatic transmission, but the Jeep's shifter moves, and has positive engagement when you go into gear. It is very tactile, feels more mechanical, and is more obviously in whatever gear (park/drive/reverse) you select. Also, if you click it over to the left, you go into "manual shift" mode, and the manual shifts are crisp, with positive physical feedback (haptics) to the driver.
Both in terms of aesthetics (less important), and in terms of physical feedback and mechanical feel (more important), I think Ineos should have developed their own shifter (or borrowed one from Jeep). I am not suggesting "Jeep is better than Grenadier" or any nonsense like that, so let's not go down that rabbit hole. I just agree with the OP that the BMW shifter is out of place in the Grenadier.