Really? How many of those devices actually had 5V batteries inside? (Are there even credible 5V Li-poly battery banks?)
Original USB (based on a quick search) specified 5V +- 5%. You’re not getting that by direct connection to a battery, and you also can’t charge the internal battery by direct connection to any common supply. Somewhere in the power brick is a switching converter.
So maybe a 5000mAh USB-A power brick can supply 5000mAh output before conking out, but I doubt it.