Why iron hulls accompanied steam power

How long did iron-hulled ships take to emerge after the first steamships, and could fully steam-powered wooden ships have persisted?

Wooden steamships did exist, but advances in boilers and engines also accelerated iron and steel production, making thinner metal hulls increasingly attractive.

Fully steam-powered wooden ships did exist, so steam propulsion did not mechanically require an iron hull. Boiler and engine production nevertheless drove improvements in metallurgy and industrial capacity at the same time. Those advances made iron and steel increasingly available just as steam machinery demanded more efficient use of internal space. Metal hulls could be heavier as material, yet their thinner structure recovered useful volume and made them increasingly attractive choices.