One balancing time I'd recommend is looking at pregens:
http://dnd.wizards.com/articles/features/character_sheets
Consider those characters at low and high levels and see what effect the house rule would have.
* At low levels, the current span is from a -1 ability modifier with no proficiency all the way up to +4 from ability plus +2 proficiency, for a -1 thru +6 span.
* At mid levels, the current span is from -1 ability modifier with no proficiency all the way up to +5 from ability plus +4 proficiency, for a -1 thru +9 span.
* At high levels, we'll be generous and assume no ability scores lower than 10 and a cloak/ring of protection to boot. We'll also assume a score of 22 is possible (from whatever source). The current span is then from 0 ability modifier with no proficiency all the way up to +6 from ability plus +6 proficiency, plus +1 magic bonus, for a +1 thru +13 span.
Of all these numbers, my issue is only with the lower end of the mid and high level spans. Having one or more saves still hovering at or near zero at level 10, 15 or 20 is strange as hell, and not the least fun.
Now let's eyeball what my current proposal does, i.e.: Con>Fort, MAX(Str, Dex)>Ref, MAX(Int, Wis, Cha)>Will. Essentially everything Kryx suggested except the aritmethic justification and the averaging instead of taking-the-best.
At low levels it is reasonable to expect a positive modifer to Con for pretty much every character. Many characters dump either Str or Dex, but very few dump both. And almost every character will have at least a +2 in one mental stat.
* So the span becomes +1 from ability with no proficiency, up to +4 from ability plus +2 proficiency, for a +1 thru +6 span. This I consider a success. It's an improvement, but without threatening game balance.
At mid levels not much change at the low end. I will still up the ability bonus one step for the sake of argument.
* So the span becomes +2 from ability with no proficiency, up to +5 from ability plus +4 proficiency, for a +2 thru +9 span. This I consider a success. It's an improvement, but without threatening game balance.
Only at high levels do I consider players to have spare ASIs to use on shoring up their defenses. Also, since it is only now they start to feel the hurt of having very low saves, so arguably only now is when they start thinking about shoring them up.
Again for the sake of argument, we'll consider a fairly well-build character. It is not unreasonable to expect at least a +4 in either Str or Dex, at least a +2 in Con with proficiency, and at least a +4 in a mental stat with proficiency. Add a magic +1 bonus on top.
* So the span becomes +4 from ability with no proficiency at worst, or +2 from ability with proficiency. The top span remains unchanged, +6 from ability plus +6 proficiency. Plus +1 magic bonus.
This leads to a trio of saves in the vincinity of +5, +9, +13.
Does this look reasonable to you, Jester?
Or have I forgotten something?
I am aware this is only a rough generalization, and that it might well be possible to create more optimized characters already at low levels.
But do you agree my general conclusions stand? That some (perhaps not all) characters will still sport a +1 low save at low levels, and that this will only slowly rise, until (and if) the character spends a feat to "plug" it.
And that at that time that character's lowest save will shift to something like a +5 or thereabouts? (Since the "plugged" save will probably scoot up to something like a +9)