The problem is with the broad language of the lawsuit and the court decision. As it stands, even though a K1 has come legally, the government really doesn't do the best job in giving a K1 some sort of 'special status' while they are adjusting. If there was some kind of rapid system that got a K1 an EAD immediately, perhaps, but as it stands there's not a lot one can do until they have the documents that give them status. A K1 is always in a sort of limbo mode until EAD or GC. This is why doing things such as getting an SSN can be a struggle at certain offices unaware of their own policy, or getting an ID through the state can be problematic.
This broad language catches out DACA, illegal immigrants adjusting, those "grey-area" immigrants that are adjusting status after a visit to sudden marriage or emergency marriage, and yes even a K1. It also is catching out other perfectly legal immigrants adjusting status as the website mentions. There isn't any distinction between legal and illegal here, any more than there is between legally grey. That is unfortunate. K1s can obtain coverage in any other state not mentioned. The only other option is to get the EAD, get on an employer's or spouse's other means of insurance, or.. well, move to a different state.