Why Hood was not designed around quadruple turrets

Were there plans for HMS Hood to carry quadruple turrets?

The discussion says no: quadruple turrets imposed demanding space and hull-form trade-offs, and were not a preferred solution when Hood was designed.

A four-gun turret is not merely a compact way to add guns. Accommodating its machinery and working space makes a ship broader, while retaining a fast hull can demand more length and expense. Hood's triple and twin arrangement is therefore treated as a product of contemporary design choices rather than a missed easy improvement. The mounting must be judged together with the hull form needed to carry it, not by gun count alone.