While possible, please take the quest to find a USB-A cable that support USB Power Delivery 2.0 (PD 2.0 for short).
I've read through the standard and while it seems that you CAN make a USB-A cable that complies with the PD 2.0 standard, I've not yet seen a single one - or a power-supply that supports PD 2.0 via USB-A.
I find quite a bunch 'though with PD 2.0 and USB-C 'though.
But I think that definitely having a USB-A-port on the charger as well would be a nice touch.
EDIT: Also a problem that would come up with going USB-A to USB-C is that with a non PD 2.0 compliant USB-A - USB-C cable charging the PF would be limited quite a bit - I'm not sure on the fallback routine, but if it doesn't fallback to the "old" PD-standard it'd charge with 5V 2A at most which would definitely confuse a huge bunch of people that don't read into this that much.