Some time ago, when I was between bikes, I came across an accident on 'twisties' out towards Skegness. We were the second car on the scene only seconds after the incident. Bike hit a caravan coming the other way. Bike and rider went under the 'van. Rider was shaken of course, with a broken finger or two; but the first thing he said when he began to speak was that his back protector had saved him - he'd felt the thump in his back when something hit him.
Fast forward a year of two - when I got back on a bike again, the first item I bought was a back protector (Knox). I find it awkward sometimes, and I lurch across carparks like Richard III (or Good King Richard as he is now); but if I'm tempted to leave it at home, I remember that unknown biker sitting on the grass verge outside Skegness and put it on. I take the foam pad out of jackets and strap on the Knox.
I wouldn't say it had to be a Knox (there may be better versions for all I know) but having seen the effects one one in action I would definitely say they are worth using over a foam pad - although, of course, I hope neither you or I ever have to put one to the test.