I think all toothpastes are, to some degree, abrasive. Water will, over time, wear down stone.

The question is: Exactly how abrasive does a toothpaste need to be to remove crud from teeth? How abrasive can you afford for it to be before it dangerously thins the enamel within the expected lifetime of a user using it at expected rates?

From what I understand most early toothpastes contained pumice. Pumice if it is too course or too frequently used sometimes removed too much enamel. Some were too abrasive. This was back in the 70s.

As I understand it none of the major brands of toothpastes are too abrasive given average use rates and normally tough teeth. Of those toothpastes ones with baking soda, because it is a softer material, were generally a little less abrasive.

I can say that the OTC bleaching agents can damage the gums if used incorrectly or too often. Destroy your gums and your newly whitened teeth fall out. I guess you could wear them as a nice necklace.