Your stated logic answers your question. If you are convinced that you will be up against a bigger A when you push with A4, then it is even more likely that you are behind with JT. I'd rather go out on Ace-high than Jack-sh*t.

EDIT: What I'm trying to say is that you want to be ahead, you don't want to be drawing to 6 outs. You will more often be ahead with A4 than dominated by a bigger A (I have no numbers to back this up).