No, that's just not true.
Light wooden shield: Hardness 5, 7 hp
Heavy wooden shield: Hardness 5, 15 hp
Light steel shield: Hardness 10, 10 hp
Heavy steel shield: Hardness 10, 20 hp
And the price difference really isn't that much. +1 AC for 4 gp? Even at 1st level that's a huge bargain. Taking armor with 1 less to AC gives you much more than that in gp you save.