So even trying one's best, half your saves would be at only +1.
I suspect one could do better.
In a game that includes feats, choosing such an array for saves is so unlikely as to be absurd and impossible to talk about seriously, only in terms of "Hey, anything's possible." ("Yay, no I have a 5% chance of success instead of 0%...)
But in that case you could use feats to get proficiency in more saves. If your priority is avoiding terrible saves, you'd presumably do that.
In either event, pretending that the player can do something effective to address this weakness is just that...pretending.
In 5e the ball is really in the DMs court when it comes to fixing any perceived systemic problems. In this case that fix could be a fairly straightforward house rule.
Tony's post that you quoted makes two significant assumptions that are not inherently true: that the standard array is being used, and that the player is going to aim for a 20 in a particular score.
And that feats aren't in use, which is a less likely assumption, IMHO, than the first two. And, feats present the most powerful player-side way to address the issue, by letting you trade stat points and/or offense/specialization/flexibility offered by other build-desirable feats for proficiency in more saves.
Assuming the array is just a convenience, as it ignores the variability of other chargen systems (but I'll happily acknowledge that I've personally found 5e to work /better/ with random generation, because you likely get an array-superior character or few who can help carry the party at the lowest levels, even if you do risk possibly getting an array-inferior character).
OTOH, I also assumed aiming for a 20, but starting with a race that gave you a bonus in your primary stat. Obviously, not everyone does both. It'd be slightly worse if you aimed for a 20, but didn't have that racial bonus, for instance - you'd be stuck with at least one +0. A MAD build that needed a second stat at 16+ would also have a bigger problem supporting it's weakest saves.
Giving up on your primary at 18 isn't completely unreasonable, 16 at the outside. That could give an ending CYA array of:
16, 14, 14, 14, 14, 12.
Still only one save at only +1, three at +2 (saves: +9, +8, +2, +2, +2, +1). 'Impossible' saves are still on the table, though they still don't strike me as necessarily at all common (the DM can choose simply to never put a DC higher than 21 on the table, even at 20th level). Quite hard saves (requiring a natural 16 or better) wouldn't seem unusual, though - nor even avoidable without making them very easy for some other characters (+11 being entirely doable at that level).
But, at no point is there a danger of the DM placing a save that is impossible for one character, yet automatic for another, the maximum gap being about 12. A clear example of BA & Adv/Dis working as intended, even in the corner case.