Yes weight was a huge factor, imagine trying to use a giant iron pan. Less mobility and of course cost. If you're a low class militia it's much cheaper to buy a shield boss and just change out the wood after a battle. Also steel had ways to go before being suitable for even plate armor. The invention of better forges and mills led to harnesses, cannons, at that point it's not really worth it.

Sources: The Norman Knight, Osprey Publishing I'll add more when I'm home, on mobile.

Physics. Wood did a better job of absorbing the impact of blows; metal would just transfer that force to the arm of the shieldbearer.

Also metal, particularly good steel was expensive. You avoided using it where you could replace it with other materials.