Question:
When the protons are close to each other, the electrons do affect each other, and the wave function above is no longer valid. But suppose you were given the true wave function, and you were once again asked to draw the blob showing the probability of finding electron 1 (using a plotting package, say). What would the big problem be?
Answer:
Since electron 2 now affects where electron 1 is, you would have to draw a different blob for every possible position of electron 2, an impossible task.