Why state naval industry strengthens purchasing power

Must a global or regional naval power control a large share of its heavy industry?

No, but direct industrial capability gives the navy expertise and leverage when judging private construction costs.

Direct control of heavy industry is not considered a prerequisite for naval power. It does provide support by letting a navy build ships itself and learn their costs. That experience gives it a basis for challenging commercial prices. Its own industrial capability can therefore counterbalance the interests of private suppliers.