To add to Drath's post; be aware that ability checks encompass more than just skill checks. Skill checks are ability checks, because they use the ability scores, but you may often be asked to make straight ability checks (make a strength check to break these chains); a strength check is not a skill check, because it's not tied to a skill, but it's still an ability check, and a strength-hexed person would have disadvantage.
In game, the only place where this would have much immediate effect would be if you opened with a dexterity hex on a target - they'd be forced to roll their initiative at disadvantage, since that is an ability check using dexterity. I don't believe the game *actually* gets this right however. Similarly we can't actually TELL if the game is using acrobatics or athletics to resist shoves at the moment, because the combat log isn't as robust as it needs to be... and stealth in combat doesn't seem to be making contested rolls against perception at all, at the moment.
