Constructs are great. Their main downside for being a BBEG is independent agency as most are created to be automatons. But that could be exploited. you could have a Marut whose golden tablet was corrupted or was written so badly that it has misinterpreted it’s goal and is now on the warpath against entire cities.

You could also have a construct that has an intelligence in it. Some constructs are simply imbued with sentience, like Warforged. And magical AI works but you could have a caster that made a modified Magic Jar and created a construct to house their soul. Now that wizard has a new body to conquer the world and you can bite his shiny metal ass!

But the immunities are nice. Generally the physicality is fixed so you can’t change their form. Exhaustion, poison, paralyzed and petrified generally don’t work either.