And yet, somehow I and my players are able to use this procedure successfully. Amazing!
I don't know if Flamestrike is suggesting this specifically, but the order of the hits matter. If you'd rolled 5 attacks serially and gotten Hit, Hit, Hit, Miss, Miss that's different from Miss, Miss, Hit, Hit, Hit. If the PC was dropped after 3 hits in the first case the last two misses would have advantage and be rerolled but in the second case they would not. So rolling them all together could be biased against your players unless your procedure includes an ordering of the dice as Oofta suggests above. But if you have a dice ordering then rolling them all at once should be exactly the same as rolling serially.