ANI is "sticky" for in-wats calls but not for any other calls. Other than in-wats ANI is an operator trunk treatment (including wireline E911).
The CLID blocking rules do not apply to in-wats. I don't believe the CLID SS7 message is even sent on an in-wats call. Lots of half-smart users dial *67 before an in-wats number thinking they are going to block their number from reaching that predatory call center they are calling. Surprise!
I think the FCC tried to explain that back in the late 1990s when they still gave a darn about making the Caller ID system working. Maybe now that we have a Democrat (and democratic) president again the FCC will once again grow to care about consumer issues.