much snippage...
Average 4d6 drop worst is 16, 14, 13, 12, 10, 9.
... more much snippage
I wanted to come back to this point because it bothered me at the time but I didn't have time to look into it. I took that time just now, and, as I suspected, this isn't exactly true at all, it's more a shade of a possible true but mostly not.
The average array for 6 rolls of 4d6 drop lowest isn't functionally possible to find without error bars so large as to render the result meaningless. What's been done, and reasonably so, is to determine what the expected average roll of 4d6k3, and that's between 12 and 13. This is better than the expected 11.5 of 3d6 by 1 point. But the ends of the PDF for 4d6k3 are still bell shaped, if distorted towards the higher values. You have a higher chance to roll an 18, for instance, but only by 1.2% (0.46% for 3d6 to 1.62% for 4d6k3). Nice, but not huge.
So, most of the discussion I've been able to find translates this 12-13 into a +1 mod, and then assumes the average across the array and says that you should expect to get a +6 total mod out of 4d6k3. (This compares to a +5 total mod from point buy, for reference.) And this is also reasonable, you should expect an average of a +6 total mod from 4d6k3.
The problem is that this is then extrapolated into a 'rolled standard array' with numbers like what you give. This is bad, no go, shouldn't do. You should not expect that array from rolling -- in fact, what you get from rolling will likely not be that at all. What you will normally get from rolling is an array that has a total mod of +6 - and even that should be taken with a big grain of salt given the variance involved. What this does is create a 2 step conversion where you take an average expected value with a high variance and convert it into a system with half of the resolution and a lower variance (going from a rolled stat average to a bonus mod average on a smaller scale). Then the second step hits where you go from the lower resolution mod numbers back into specific stats, but add in a bit of arbitrary choice because you have to pick between two non-equal values to represent the mod in a stat. This loses information twice AND adds an arbitrary element.
For instance, for the +6 mod I could pick: 17, 15, 13, 13, 11, 9 or I could pick: 16, 14, 12, 12, 10, 8. Both are valid transpositions using this method, but I'm pretty sure no one will agree these are remotely similar sets of stats, especially with how racial modifiers and ASIs can interact with stats at the +1 level (if all ASIs and racial bonuses were +2, it wouldn't matter).
So, to wrap back to the point of the thread, the "average" array you selected for the example bladesinger on 4d6k3 is anything but -- it's a good bit of arbitrary choice lying on top of a method that loses information about what 4d6k3 actually rolls. You MAY roll that set, but you probably won't -- it'll be different numbers. All that can be said is that,
on average (and that's doing a lot of work here), you'll get a +6 total mod bonus.