Would the Royal Navy have built an F3-type ship if the Washington Naval Treaty had not intervened?
Short answerProbably not. Without a treaty limit, Britain had little reason to accept a 35,000-ton compromise instead of building a 40,000- to 45,000-ton capital ship.
NotesA comment imagines F3 facing Amagi, Kii, and Lexington in a world without treaty cancellation. The design itself depended on a constrained displacement environment. If larger ships remained legal and affordable, designers would move toward a G3-scale answer rather than preserve F3's compromises merely to stay near 35,000 tons. The treaty creates the requirement that makes an F3-sized capital ship rational in the first place.