Whether characters are "guaranteed to suck" depends on where one draws the line on "sucks". Clearly, the characters will have mid-level stats. If you plan on taking a spellcaster up to the highest levels, you'll need a 14 or 15 spellcasting stat (15 to cast 9th level spells when they become available at 17th level, or 14 to use 8th level + metamagic for your 9th level slots until you hit L20 - unless you get a stat enhancing item).
That's 6 - 8 of your 15 point buy. With 7 remaining, you can have 3 10's and 2 8's (one can be an 11 or a 9), or 12/10//8/8/8 (again, add one to one of those stats). Drop that big stat to 6 and you can have a 14, or one more 12, or one less 8.
Or you could have a slate of 10's with one 12 (or 13 - for feat qualification), and be pretty much normal, stat-wise.
Racial bonuses become much more relevant, it seems to me, under this model.
What do we set the point buy at for NPC's? Maybe the typical NPC has assumed stats of 8's across the board. Some might get a boost (maybe Bandits get 6 points, so they get a 12 STR and a 10 CON or DEX). It's not just the PC stats, but also the NPC stats, that set the bar for "sucks".
Characters who are pretty much normal, with either one standout ability or pretty much normal across the board, stat wise would be the norm. I agree they probably rely on one big stat, so we're largely back to the old 1e structure where Paladins and Monks are pretty rare, needing great rolls (or, esp. in point buy, picking which abilities they will focus on).
Do characters really NEED 14/14/14/14/10/10 (or 16/14/12/12/10/10, or 18/14/12/10/8/8) to be considered "competent"? When we tried to port characters over from 2e, we quickly stopped looking at the characteristic, and looked instead at the bonuses. You previously had an 18/76 STR and got +2/4? Well, that's an average bonus of +3, so you have a 16 STR in the new model. Used to have DEX 15? A +1 bonus is a stat of 12. That brought a lot of characters in at a reasonable budget, probably above 15 point buy, but not typically at 28 point buy levels unless the character's 2e stats were pretty incredible.
The two keys, to me, will be:
- comparable PC's (dice rolling carries the potential for disparity with good or bad luck), though allowing re-rolls based on not meeting a de minimis total bonus and maximum bonus would take out the lower end;
- challenges set at a reasonable level commensurate with character power.
I agree, though, that a bonus becomes a BONUS under this model, not an expectation. In fact, I might go so far as to re-set the model to make every success roll one higher, and every bonus one higher, so 8 is +0. Happy now? You have no penalties. Save DC's are 11 + Spell Level + attribute modifier, and AC is 11 + bonuses.
Oh, and note that most opponents, if designed with the same point buy, will have lower bonuses to hit, to AC, to saves and to save DC's. Monsters will be tougher, as their numbers will not change. Simple fix? Maybe you have three, rather than four, encounters in a day.
In fact, it seems like this is a possible mitigator for the 15 minute day. You will have less resources to spread over the day, so if you can restrict yourself to one encounter an day, it need not be quite as challenging to make the characters sweat.
Would it be my first choice? No, not really. Would it be guaranteed unplayable? Certainly not. Could it be a great campaign? Sure - especially if players realizing their stats will no longer differentiate the characters focus more on their personalities.