T'is annoying, but endurable. I do both; collect my fragment producing buildings manually until I run out of BG chances, then pay the 5 dimes to collect the rest.
One method to cut down on the pop-ups when collecting, is try to lump the frag producing buildings together in your city. Make sure your FP bar is empty. Not a requirement, but it helps. At least make sure you have plenty of room for what you are collecting. Then, instead of clicking on them individually, click on the first one and quickly swipe across the rest while holding the mouse button down. It may take some time to perfect this, but it does work.