The frame flex leading to the tire rubbing has little to do with the flex of the cranks. That is flex in the frame.

If you replace the ST bb with a hollowtech, you also need new cranks.

IMO, there is little to be gained by upgrading. The difference is there but not all that much. There are almost certainly better places to spend upgrade dollars.

Wait until you need to replace the crank or BB for other reasons.