I think you're over-stating this. What you've probably read and heard is that the rear brake doesn't give nearly a much stopping power as the front. But to say it doesn't add to it is just wrong. A lot of people, because of misguided fear of going over the handle bars, use only the rear brake (my wife and daughter two examples). They stop just fine.

I guess I'm just wondering if you have a brake adjustment issue. My wife is 5-1, late 50s very small weak hands and uses Tiagra STI's with rim brakes no problem. But of course, she's also small in stature so that's a big difference from your situation and probably changes it totally.

But if it were me, I'd have the entire braking system checked out before putting both levers on the front brake and having the rear brake be an after thought.