This is only an anecdote, but following are the rolled stats from my last two tables (5 players each). There were no rerolls, no shenanigans, just straight 4D6k3. The stats are presented at the order rolled, but afterwards the players rearranged as they saw fit.
First set:
16 11 17 5 12 8
15 7 13 11 16 11
14 6 15 9 16 15
9 11 10 15 17 13
7 11 11 16 12 14
Second set:
13 14 10 14 9 15
13 12 13 13 15 8
16 7 16 9 11 17
8 15 14 14 13 6
11 15 13 8 12 14
The first set average was 12.1, slightly better than standard array. The actual totals ranged from 69 to 75.
The second set average was 12.2666, and totals ranged from 70 to 76.
I would say this is not what usually happens, as I have seen on older games at my table a PC built with scores such as 14 12 12 10 10 10 (no negatives, but quite dull lowish distribution), playing alongside a powerhouse 10 16 15 16 13 12 PC. But, in game, it worked out just fine.
We have let someone reroll on other, more dreadful cases, such as a guy who rolled a best 13 and the sum of modifiers from all scores was 0. He didn't complain or ask to reroll, but I told him to dump it and roll again as I would not be excited to play those scores were I the player. And I had this friend who rerolled a 12 10 4 17 14 15 because he could not withstand the 4 in his sheet. No problem, his second set got a slightly lower total, but the minimum was a 6, to which he was okay. I found it funny, because I would love to use his original set with the 4, as it also had some nice strengths.
There is, sure, a chance that scores will me more spread, and differences between PCs are more pronounced, but frankly, in all my years playing, that hasn't happened often enough to become a problem. Rolling 17s is already quite rare, and even a single 18 is so special that everybody gets excited when one player has it. Conversely, very low stats rolling 4D6k3 is difficult to happen. Even the sets with lower average than the standard array usually have one or two nice higher numbers, which suffices to make effective PCs. This has been my experience for decades already. I have seen people sharing that where they play there were all those 18+ str fighters back in AD&D. For us around here, they were really rare and memorable, and I don't even remember someone rolling a 18/00.
But, as I stated, this is all anecdotal.