K2 and K3 were formidable designs rather than a final practical limit

Were the K2 and K3 battlecruiser designs close to the practical limit for that type of ship?

No; they were ambitious but viable, particularly with 16.5-inch guns, and could have entered service if Britain chose them.

The K2 and K3 battlecruiser studies should not be treated as the final practical limit of their type. Either would have been a formidable alternative to the Admiral-class route and would have changed the bargaining position at a later naval conference. A 16.5-inch battery appears more practical than the 18-inch option. The ships were ambitious but still buildable, which separates them from a design that had crossed into operational impossibility. Their completion would have made the resulting treaty settlement very different.