The Crimson Binome
Hero
There is, indeed, a variant rule where you might sometimes apply a different attribute to a skill check. The default assumption is that every Athletics check is a Strength (Athletics) check. If the DM really thinks that a different stat is more applicable, and that opening up the possibility of alternate skill bases is appropriate for the game being run, then the DM has discretion to ask for a Con (Athletics) check instead. It really is the exception rather than the rule, though. I wouldn't expect to ever see such a thing listed in a published adventure, in the same way that no published adventure will implement slower healing times.There is no such thing as a "skill" check in 5e, just ability checks to which your skills may apply and thus allow you to add your proficiency bonus. Also no skill is tied to a specific ability, if you can make a case why that skill would apply in the given situation, it does not matter if it is a strength or Con check, you still get the proficiency bonus if it makes sense. Some skills logically lean towards one or more ability scores, but they are not tied to it is my understanding. I'm pretty sure the DMG even gives an example where in different situations a person could apply Athletics to either a Str or a Con check, as long as it made sense.
It's never on the player to make the case, though. It's only ever a tool for the DM to use, should circumstances warrant.
There are two possible explanations for why the system is the way it is. The Watsonian explanation is that knowledge of arcane phenomena simply does not aid in your ability to overpower another spell, unless you have very specific training in how to do so (as an Abjurer does). The Doylist explanation is that we don't want spells to be dispelled too easily, and we want to throw a bone to the Abjurers who really should be the star in this situation.So in this case I don't see why you would not be able to apply arcana skill to say ya, I should be able to get this bonus on this Intelligence check.
Note that, if you let Proficiency factor into your check, you have a 65% chance of ending a 9th-level spell effect by expending a 3rd-level spell slot. If you let Abjurers double-dip their Proficiency, then they never need to uprank a Dispel Magic in order to end a spell of 8th-level or lower, and they can fail to end a 9th-level spell only on a roll of 1.