This might just be a choice of words, but when you say charge and discharge battery, I separate what you hold in your hand into two aspects, so not disagreeing but expanding the problem.
Inside a USB powerbank is electronics and chemical energy storage substance "battery". When you use a powerbank to recharge the battery, the electronics are producing a progressively higher voltage and lower current to the chemical energy store. When you use the powerbank as output, electronics take the energy out and progressively step up the voltage output as the chemical energy lowers its voltage.
It would not be the battery which charges and discharges concurrently. There is a mains power (110V/240V) electronics which can give the battery just what it needs and no more, with whatever energy is left after servicing the USB output, which is a more complicated role for electronics to juggle both concurrently than serving one role at a time.
Analogy, you have some food you just bought, you feed the family what they want til full, then put the rest in the fridge to store for another time. Regardless how hungry is the family, you are not putting more stress on the fridge.
This is about electronics, not batteries, or about how smart you are knowing the family is full and its time to open the fridge door.
Because more intelligent electronics increases the design and manufacturing cost, it increases the cost of the powerbank with the capability.
No electronics is 100% efficient, I see figures of 80%-95% so there is heat of doing anything, so if you had both electronics to produce the constant 5V USB output and the steadily increasing voltage (say from 3.2V to 4.2V) of the chemical energy store, this increases the total heat inside the packaging. Given the chemical energy store oxidizes and loses capacity faster when exposed to higher temperatures, you will either need a bigger device, or active cooling (fan) or accept more device failures / accelerated aging.
I side with Anker on this because it lowers the costs, and keeps the sizes smaller. I tend to be perfectly happy with a dual USB socket Powerport and a Powercore and I plug the Powerport and Powercore together, this separates the heat.
The Powercore Fusion is the 1st of the kind from Anker with the electronics to do both, but observe it is only 5000mah, rather large and a higher cost for its capability, only 10.5W.
There are youtube tutorials on the electronics associated with step-down voltage and step-up voltages, it isn't that complicated, but you can soon appreciate the challenges with a hybrid product.
I do expect Anker will learn lessons, and possibly with the IQ 2 being more efficient, that a better Fusion will emerge at some point.