There's already a Flash upgrade service for iPhones available in China (similar kind of BGA chip). Which is kind of terrifying, the Flash on the iPhone has undersell so it has to be milled off on a CNC router, but apparently the process works quite reliably.
Where there's a will, there is a way, and all that...
I don't remember if the Psion was BGA or not; I'm guessing not which makes soldering it substantially easier.
In a similar vein, you could double the RAM on the original Xbox by soldering a second memory chip to the unpopulated pads on the underside of the board.
Apple caught onto people getting storage upgrade for a reasonable price and made it so those phones will be bricked if you update them to the latest iOS. Scumbag Apple as usual :(
Where there's a will, there is a way, and all that...