I recognize why power banks can't charge and discharge simultaneously. But surely, with as cheap as integrated circuits and voltage regulators are, we can have a power bank that can be charged while it redirects some power around its cells to a device on the other side?

Sure, both would charge at half the speed. But if you only have one brick, it's better because you don't have to swap the cables halfway through. Plus, if your phone charges faster than the power bank (which it almost certainly will), you can unplug it at full charge before the power bank is done and let the bank finish- or unplug both and have a fully charged phone and a partially charged power bank.

Made even better, what if we integrated a power bank into a GaN charging brick? Plug it into the wall, use it to charge your devices every night, the smarts inside it regulate the battery with charge/discharge cycles; but then when you're ready to go somewhere you just unplug it from the wall, flip the prongs back inside, and go. Maybe you could even push a button to tell it to charge to full. It would also be a UPS of sorts, since it wouldn't know the difference between a power outage and you taking it on tour. Yeah, it would need to be kinda big and bulky when it's on the wall, but the convenience of not needing to track it down and plug it in before you go on vacation would be worth the hassle of needing to plug it into the bottom outlet on a power strip. Something about the size of a MacBook charger, but with all the high-wattage stuff swapped out for battery cells.