Especially given its description, the Charmed condition seems like something that high DC Persuasion check should do. Then the various methods of spells would be various ways to gain proficiency, expertise, advantage, or substitute a different ability for this check − but even these spells still need to make an Ability (Persuasion) Check.
Likewise the Intimidation skill can induce the Frightened condition.
When I think about Intimidation, the same capabilities to appear tough and scary, are the same capabilities that can appear strong and confident in order to boost Morale. Thus one can actually use the Intimidation skill to end the Frightened condition in an ally, or even to restore hit points to allies via Morale. These might be surprising uses of Intimidation, but are sensical given what the concept of Intimidation assumes.