Those USED to be a hot idea. I should know, I have two of them sitting in my junk drawer, one two-cell unit from Radio Shack (yeah that's how old it is) and one four-cell unit from Rayovac. Hell, I remember having a ONE-cell Energizer model. And they were fine, at the same time that flip phones or Nokia candybars were the top of the line, before power gulping smartphones and back when the USB standard for power delivery was only 500 milliamps. Now? They can't compete. What your friend said about lithium ion batteries is correct. Today's phones expect four times the charging speed, which even the four cell Rayovac cannot provide. But, if you insist, it's apparently still on the market.
Your product page claims to be able to output at 1.5A to the phone. 1.5A at 5 volts from 4AA? Good if true, but I suspect that will heat up a lot.