Something to take in mind is that yes, they would need to retrain the models from zero, but if they did it in any kind of basic decent method they should have backups and versions of the data they used to train and they would need to retrain everything with a subset of the original data. Then, the optimizations they have already applied to the system should be able to be reapplied in the same manner and the product should be somewhat similar. Another thing would be to design a de training process, where you generate an input from the “must be deleted” input that when trained acts as some sort of “negative input” and the model ends up in the same place it would have ended up if it were not trained with the “must be deleted” data.

I bet you that if governments act harsh enough tech companies will develop some sort of “negative training”.

In the end this is a solvable math optimization problem, what input do I need to feed the already trained model for it to become the equivalent model it would be if trained without the requested data.

We could even create an ML model that computes a “good enough negative input” from several examples, since testing the quality of the results is quite simple, and we can train it with several trained model examples. This model would be fed with a base model, some input data and another base model trained without that data.

All in all, AI companies will tell you that this is very hard because they would essentially be investing hours and development to create a tool that makes their model worse instead of better, so expect a lot of pushback.