Nonsense. There's a fundamental requirement that for a model to have utility, it must have access to relevant data. If you truly find a leak-proof way to block certain values (which is borderline impossible in itself), then you make the model significantly weaker or outright useless if those values aren't uniformly distributed across the input domain.
And if you do have leakage (and you almost certainly do), then direct re-identification becomes a trivial problem and we're back to square one.
Synthetic data generated from statistical analysis of real data is either worthless or leaky. One of those two conditions is formally guaranteed to be true.
GP is correct that a viable synthetic data generator basically has to have already solved your problem for you, and in that sense it just becomes your model which is trained on real data. Training an additional model on top of that model doesn't add any privacy or mitigate reidentification.
Guaranteeing that certain values are not passed is both useless and trivial. I can easily satisfy that by simply adding 0.1 and a space character to all values in my dataset even though that doesn't remove any of the sensitive data.
You can see some of my work here:
https://medium.com/capital-one-tech/why-you-dont-necessarily...
The reality is, you can guarantee certain values are not passed. That’s fairly easy, what you can’t do is block general trends easily in synthetic data - else the model can’t learn. So you have to be willing to accept that “leakage” when using synthetic data.
If you accept that leakage, then you can actually improve model performance in some domains. See ubers architecture search blog, there’s a lot of material (also from Uber) showing this.
Regarding cost of training, yes model training costs could increase. Although, I’d suggest much much less than 10x more like 50% or something. Is that worth it for privacy?