My two cents: Interrupting a spell should have approximately the cost and difficulty of deflecting an arrow (that would otherwise hit), blocking a sword-stroke (ditto), disarming an opponent, or breaking an opponent's weapon. It should have a lesser cost & difficulty for a spell directed specifically at you, and a greater one for stopping an area-effect spell or if the caster has to pay a cost beyond just the lost action.
Agreed - for spells that accomplish the same thing as a sword or bow attack. What about spells that turn your insides into your outsides? Some spells accomplish quite a bit more than the above examples.
The problem I see with this line of thinking is, once you say "yes, of course, magic should be interruptible", I can imagine players asking if other things can be. Can I interrupt someone using a bow or crossbow? Interrupt a sword slash? Sunder or Disarm weapons? Target the wings of a flying creature to bring it down?
Some of these things appear as different rules (in different games). It makes sense for some additional rules for spellcasting interruption to appear in these games. My nitpicks with these are A) they often include loss of spellcasting power despite no spell occurring, and B) more rules to remember. Or more likely, more textbook-on-table time.
Making a way to actually interrupt spells into a Fighting Style, Maneuver, or Feat (or something similar) would be perfectly fine, but how many people would actually go out of their way to get such an option as opposed to other things they could do?
Me, for one. If I can take a little training (feat?) and have the ability to disrupt some potentially life-ending events, I'll sign up!
The question then becomes, "what is the equivalent of a 3rd-level spell slot for a non-caster". Because that's the going rate for Counterspell.
Now one could say that Martial Counterspell doesn't have to be equal in power to Magic Counterspell, and it could be easier to pull off, but then the question becomes "why have Counterspell?". Because if countering spells is something anyone can do with a weapon, then the casters could do it as well.
To pull this away from D&Dese a bit, a Modos 2 counterspell, Dispel 1, is a one-action spell (hence the "1"). It's just as fast, in action economy, as throwing a dagger, and as such, it can also occur as a reaction. So throwing the dagger might be a non-caster equivalent, but there's no rules-support for a dagger attack disrupting a spell, besides rule zero. There's another twist: taking damage doesn't even mean getting hit by a dagger, so what would actually be the interruption?
What would Martial Counterspell be? Probably a called shot. "I shoot the caster's spell book/casting hand/staff." Which, yes, casters could do as well. As GM, I'd tack on a bit of difficulty to such a reaction. Which adds value to Dispel 1, because its difficulty increases with the level of the spell to be countered. So countering a level 1 or 2 spell with Dispel would be easier than throwing a dagger or shooting an arrow, from a luck-of-the-dice perspective. Also, while casters could use the martial counterspell as well, a warrior is likely to have more skill at it than a spellcaster would.