If tags were added to each bitcoin that was mined, then you would eventually result in infinite tags to a child coins after used coins are mixed.
Is it now impossible for any transaction in bitcoin to find out through a retrospective study in which blocks all the components were extracted by the miners? I do not know how difficult it is to calculate, but since there are all inputs and outputs in the circuit, it is certainly possible.
The protocol, by the way, could provide that in the bitcoin chain, the additional value from the manufacturer lives no more than n blocks, so as not to really load the native network and motivate miners to immediately output the mined bitcoins into the side chain to clear the bits from the labels and receive the manufacturer's tokens.