CAP's A isn't a very useful thing at all. There's nothing stopping a database from being both Consistent and (common-sense definition) Available on the majority side of a network partition. It just can't be available on both sides, which is unfortunately the definition from the CAP proof from Gilbert and Lynch. The proof isn't wrong, but it is extremely misleading if you go into it expecting the common-sense definitions.

There's also nothing stopping systems from accepting commutative writes, and hence being available for writes on both sides. Similarly, if the system accepts no writes it can accept reads on both sides without breaking the law.