I would love to see that too, unfortunately for now TPU on AMS is not reliable and that’s why Bambulab do not allow it and I think they will not go back for some good reasons.
I have made several tests and hours of work on this problem and I will continue, and I can confirm that TPU can work in certain case, with certain brand, but it also fail too often and stuck the AMS.
So Bambulab IMHO cannot allow TPU in AMS because if they do so, they will instantly get hundreds or maybe thousands of complains asking for AMS replacement or such.
Let me be clear, I would love to print TPU easily from the AMS (without fooling it using another kind of filament) and will continu to try to find a reliable solution with the less required modifications. But commercialy it would not be a good decision to allow it with the actual AMS.
Anyway you can still set another kind of filament to fool the AMS and print TPU from it using good settings, but depending on your unit (specially tensioning spring of the AMS output motor), your model, retraction settings etc… it may often stuck the AMS.