Recognizing that your players would rebel if you tried to make them do 3d6-strict: 4d6-L, rearrange to taste,
also produced fairly cookie-cutter characters. I've seen a very nicely presented statistical analysis of the expected values for 4d6-L; you can view it yourself
here. Long story short: the standard deviations for the first few 'highest dice' are small, and the curves have such a thin left-skewed tail that almost the entirety of the distribution lies in the 12+ range (for the estimate of the highest die, it's something like 90% lies above 14!) And being able to arrange your stats to taste means that you'll always see people put the lowest stat in the thing they need least, and their highest stat in the thing they need most--exactly as would happen in point buy or an array. In fact, the so-called "elite array" used in 3e and (without that name) in 5e (15, 14, 13, 12, 10, 8) is slightly below the expected output of 4d6-L/rearrange (16, 14, 13, 12, 10, 9), which is itself also slightly below the 4e standard array (16, 14, 13, 12, 11, 10).
So...yeah. Allowing stats to be rearranged or modified removes most, though perhaps not all, of the "anti-cookie-cutter" effect of rolling stats. Unless someone gets an utterly fantastic roll (or cheats, which IME is strongly incentivized by asking for rolled stats), you'll still see "the same dump stats over and over and over and over again." And unless someone gets completely shat upon by the dice, you'll still see the same priorities for best stats, over and over and over and over again. And, on average, characters will trend toward the mean--so while no individual character
has to look like the expected value of 4d6-L, they'll cluster around those values pretty well over the course of a long gaming career. In a game where stats matter a lot, and where it's very easy for hurt feelings (or guilt) to arise from a noticeable gap between the worst-off character and the best-off one, I just don't see the benefits even remotely outweighing the costs.
Now, technically, you didn't actually
say you allow them to rearrange, but I've never heard of 4d6-L that didn't include it so I figured it was a safe assumption--please correct me if I'm wrong on that.