Would purpose-built landing ships appear without the war?

Would navies develop purpose-built landing ships such as LSTs in this timeline?

Yes, especially LPD-like ships from British and Japanese prewar work, though the exact wartime LST form is less certain.

The Royal Navy was already the leading Western service in amphibious-warfare design and had concepts resembling a landing platform dock on drawing boards in 1939. Japan was following a related path through its own specialized amphibious ships. An LPD-like type could emerge from those lines, and similar American studies are plausible even though no designs were identified in the discussion. These durable prewar requirements could produce different ships from the mass-production solutions created by World War II.