Might have been interesting if they'd allowed you to page out the ROM to access the extra 16K - load a small routine from tape that contains your own tape loading routine, swap out the ROM, load the rest of your app, bob's your uncle. Would have needed some shenanigans to swap in the ROM on reset, obvs.
[0] http://www.breakintoprogram.co.uk/hardware/computers/zx-spec...