Even though our history is marked by many different phases of free trade and protectionism, I think it would be more honest to say that our country has prospered in spite of trade restrictions. Mainly because we have been laissez faire within our own borders.
Since WWII, we've been, for the most part, a free trade economy (thanks in part to Smoot-Hawley). Adjusted for inflation, our household assets have increased from just $6 trillion in 1945 to more than $60 trillion today. There is no doubt that freer trade has contributed greatly to this incredible building of wealth.
If you also look at our history you'll find that a lot of third world countries of the past have now become valued trading partners. Why would you would want to keep third world countries impoverished and unable to ever buy any of our value added goods and services?
Who would that be, Mexico? Their greatest exports into the US to date continue to be drugs and illegal aliens. Simply transferring American wealth to these countries is doing little for them or us. If they're not capable of creating wealth on their own to begin with like Europe, Japan, South Korea, Taiwan and North America have then there's little we can do for them.