spell DCs do scale with levels, but no other effects of the spells.
While in 3e, a fireball scaled by increasing its damage potential, in 5e it scales by increasing its "to hit".
In 5e it scales with slot, and you get more & higher slots as you level. That reduces the 'Quadratic Wizard' problem of 3.5 (and earlier), when you scaled with level and got more slots as you leveled.
There's no need to 'make up' the lack of damage scaling by picking on poor saves, because there is no lack of damage scaling: the caster keeps getting higher and higher level slots.
In 5e, at level 10 the spell is a little bit harder to resist for someone not proficient.
Which is an issue, because it's fallen from a top-level spell to a mid-level spell. It is supposed to be getting, relatively, less effective not more.
The suggested +0 to +4 to saves will cancel caster progression.
No, it will just keep the progression from snowballing. As the caster levels he gets more and more powerful spells, if all his spells also became harder for same-level characters to resist, he'd be flirting with the 'Quadratic Wizard' issue, again.
If the designer wanted that scaling...
The designer comes right out and says he wants us to use the rules as a starting point. When answering the question 'is there a reason not to give everyone save proficiency,' the objection 'well, if they were meant to the designer would've given them that,' isn't relevant. This edition is open to house rules and variants.
I'm seeing mainly positives with this one. It means PCs aren't forced to spend ASI's on stats that are contrary to character concept, just to avoid becoming overly vulnerable when they have to save with that stat. It means high level PCs, at least, get to feel a little bit more heroic after 20 levels of death-defying adventures. It makes it a little less likely that one PC will sit out the whole level 20 capstone climactic battle because he needs a natural 19 to come out from under some low-level effect a flunky dropped on him.
The only downside is it removes one of various arbitrary mechanical distinctions used to differentiate classes this time around. It's not a big one, but the +2 for good saves, +4 more to all saves over 20 levels (prof-4 for non-prof saves), idea takes care of that.
Are some spells unfair against certain kinds of monsters?
Don't care, really. Monsters don't need to have classes or be statted out like PCs, and DMs are certainly free to change 'em or make up their own. They can have appallingly bad saves in one or more areas if the DM wants - or not.