Arguably carry capacity is important, but the game has two levers. Super generous or the highly restrictive Encumbrance variant.
Ability checks and saves are meant to be the balance point for having bad ability scores, but these tend to seem punitive- nobody can have good numbers everywhere, and I doubt a character with all 12's and 14's will feel happy about their decision, even if they have bonuses to everything.
The problem is, some saves are important and others are less so, based on frequency and effect.
Strength saves are infrequent, and unless you're about to be punted into a pit or off a cliff or into a fire, the effect is usually minor.
Dexterity saves are common, but the effect is usually damage.
Constitution saves are common, and the effects generally suck.
Ditto for Wisdom.
Intelligence and Charisma saves are rare, but you really don't want to fail them!
But then on the ability check side, some Skills come up more often than others, though this varies based on the campaign.
And then passive benefits, well, Strength has one and is important for heavy armor and weapon users.
And Dexterity doesn't have one, but it does affect initiative as well as being important for light armor and weapon users.
Constitution adds some staying power. But you really don't need a lot of this, because 5e is very generous here.
Intelligence, Wisdom, and Charisma passively do nothing, but are important for spellcasters (I'm not including passive checks here, even though passive Perception is common, because while that might be the best skill, skill use can be variable, as already stated).