Your charts don't really show that.
If you want we can crank out a quantified strength of correlation with an online regression analysis (applet here), but we'd first have to agree which data represent tariff protection and which equal employment. Not a problem; you said-- "...GDP improvements have been sloping down and Unemployment has been sloping up since about 1950. I think that has more to do with trade policy..." --so either you've got supporting numbers we can both accept or you've just got an unproven 'feeling'.
"Tariffs are obviously taxes with no proven benefit."
Ha! Our founding fathers didn't think so
Sure they did. Check out the total repudiation of protectionism in all forms with this link to Tariff Policy published in 1779 by America's Founding Fathers Publishing Trust. OK, I lied. Seriously, we both know there were many founding fathers, some liked things like slavery and protectionism and others preferred freedom. The bottom line is when they all sat down to vote, they agreed to send John Adams to Holland to set up America's first embassy to borrow money and work out an international trade agreement.
Suppose you have 4 sons and three of them pay their own way, but one just got downsized and doesnt have a job. You hire your lawn mowed at $30 a week. Your son needs $40 in gas money a week to go to school. Youre committed to providing him gas money if he cant earn it himself.
Do you hire your son to mow the lawn for $40 a week? Or do you continue to hire it out at $30?
Most would say make him mow the lawn. Youd save the $30. And would only be out $10 a week when you would have been out a full $40.
Buying imports during periods of unemployment are just like that. Were paying $40/week to unemployed Americans so that we can continue to buy the cheaper goods from China for just $30/week. It doesnt make good sense. (numbers are for illustrative purposes only and not real world.)