"Well, for shots down the line a 3B that throws y would be a huge benefit. He should be able to play off the line more and get to hard hit balls right down the line."
That is so wrong. If you are right handed try this. You play first base, I will hit a ball down the line, you field the grounder moving to your and try throwing the ball with your right hand to third base. You will then understand why a handed third basemen is not viable.
Their is multiple reasons why a handed third basemen is not viable at the major league level. Right handers can throw on the run with balls hit down the right field unlike handers who need to stop and reposition themselves to throw the ball. Same goes with bunts, a right handed third basement can throw on the run while a handed third basemen has to either backhand the ball with reduced speed, or stop and rotate their body. At the major league level a second can be the difference between a hit and a out.