So DC 19 saves are off the table, then?
Off the table in what sense? BA says you should view a DC 19 save as one that PCs will almost certainly fail. That doesn't mean you can't have a DC 19 save to avoid some horrible fate; but you shouldn't assume that everyone (or much of anyone) will
succeed on that DC 19 save, and it shouldn't grind the adventure to a halt if everyone fails. It's supposed to be a bonus when the PCs have awesome saves, not part of the expected baseline.
If there's some hypothetical class that gives double HP but saving throw proficiency in
nothing, you should be able to run your adventure with that class and have some parties still succeed and have a fun time playing.
That is not how it works with attacks, though. PC attacks /do/ scale very consistently with level. So do the saves PCs force and the save DCs they likely face.
Some of them do, some of them don't. The system doesn't assume they will, and a DM writing an adventure with bounded accuracy in mind won't either. You could wind up with an entire party of minionmancers whose main attacks are all by proxy, and no better than +3 or +4 to hit. You may have noticed that MM monsters like dragons are still quite killable with a +3 or +4 to-hit, especially if you have sufficient quantities of minions. Or you could wind up with a party of roleplayers who like to play strong lore bards, charismatic enchanters, and intelligent war priests.
And the saves they "likely" face are entirely a function of whether or not the DM is respecting bounded accuracy. That's my point here. If 15th level PCs never make a DC 10 save, only DC 19+ saves, that's entirely on whoever created their adventures. 5E is written so that you can write fun and challenging adventures for 15th level PCs (using large numbers of) CR 0-5 monsters and it will work just fine; if you're choosing to always employ only CR 17+ monsters, you're not using bounded accuracy, and your experience will be skewed.
Unlike skill checks, they can't have only the 18 CON, fort-proficiency character make all the poison saves while others 'help.'
You can't necessarily do that with skill checks either. If only the Str 18, high-Athletics guy can climb the cliff when slavers are chasing them, everyone else is going to get captured (or have to fight off the slavers without the high-Str guy). Therefore you shouldn't use ultra-slippery cliffs just because it's a 15th level party; you should choose a reasonable, naturalistic DC based on what the cliff is really like (say, two consecutive DC 10 checks to climb the 30' cliff; each failure results in 2d6 falling damage and a need to start over). That's just one example: it could just as easily be Stealth checks to sneak past the golems guarding the forbidden temple entrance, or Constitution checks to stay afloat for hours in freezing water when your ship sinks, or Deception checks to bluff your way into the enemy's headquarters.
If you happen to construct your adventures such that skill checks are always bypassed by a single roll, that is again on you the adventure-designer, not on Bounded Accuracy.
But, like skill checks, when a low-DC save (typically 13 is as low as it goes) is called for, the good stat, proficient PCs can still fail it. There's really no danger of making low DCs fall off the radar for everyone. The more ambitious 'fixes' mentioned here might give the worst-save PCs a +2, 3 or maybe +5 at 20th level - they'd still have to worry about even DC 10 nuisance saves.
Under Bounded Accuracy, a bonus is actually a bonus. Some guys are just so good that they will
never slip on ball bearings; other guys get really good at killing dragons, but have just as much trouble with ball bearings as ever.
You can give everyone +5 to all their saves and it won't "break" bounded accuracy, because bounded accuracy is a DM-side (and/or designer-side) activity about avoiding certain assumptions. If those assumptions happen to be true anyway, the PCs will have an easier time of it than otherwise. So I'm not arguing against giving PCs whatever bonuses you want to--you can, and I don't care. But I am arguing that if you're actually employing bounded accuracy in your adventure design, you don't
have the problem in the first place that makes you want to boost everyone's saves in every attribute. You're not expecting every PC to be equally good at resisting every threat, and you're not using a "DC treadmill" that makes PCs fall behind if they don't boost every stat equally to match your treadmill's expectations. Higher-level PCs are more specialized than lower-level PCs, really strong in some niches and perhaps weak in others, and that's okay.