I simulated 100 screens with different numbers of pixels where the probability the first pixel is bad in a screen is p0 = 1e-6 and the presence of each bad pixel increases the probability of the next one by the same amount (ie probability for a second bad pixel is 2e-6 and for last pixel is p0*number_already_bad_px). A screen was accepted if it had 0 bad pixels. The results look pretty much the same:

  num_pixels frac_accepted
       1e+01          1.00
       1e+02          1.00
       1e+03          1.00
       1e+04          0.98
       1e+05          0.89
       1e+06          0.32
       1e+07          0.00

Of course this was just a convenient scheme to simulate. The greatest number of bad pixels was 86k for the 10 million px screen (so chance the last pixel was bad was ~9%). It does show that the independent pixel model isn't necessarily very far off though.