If a GM can create a game in which martials are functional even though they don't have magic, then a GM can also create a game where casters can function even if they can potentially be interrupted.
But thet needs to be accounted for in the game design itself.
Fights would need to be made easier, because your remove a lot of power from the party with such a change.
A hard encounter would become double deadly if the casters are nullified.
Like in my campaign where I play a wizard. We have no martials, but we can still win, even though a more balanced party would probably be more effective.
But the proposed change of being able to easily interrupt spells would kill that party instantly.
At the moment 5e is playable with any class combination. You can play the game with an all caster, all martial or even single class combination and still be fine and the DM doesn't have to rebalanced the challenge-difficulty, because a hard encounter will still be a hard encounter and an easy one an easy one.
An all fighter party is in the same power category as an all wizard party, the differences are in the 10-30% range.
With the proposed change, an all wizard party would loose 80-90% of its power, because all their spells would be interrupted. It is a difference of aa magnitude in power level.
That would be needed to be accounted for.
At the moment in 5e, all classes are equally powerful. The difference between the worst and best class with the worst and best subclass being maybe 50%.
The proposed change would instantly make all casters be 10% as effective because they can't reliable do their thing anymore. Because without spells casters don't have any power at all. Without spells a casters is maybe as effective as a commoner in a fight.
You suddenly have classes that are a magnitude more effective and powerful than other classes. The game balance would be totally utterly destroyed.
In that particular combat, yes. They got ambushed and swarmed, which is always bad news for the backliners and even worse news for this particular party who are, it seems, all backliners.
And in that instance with interruptable spells the my party would have been TPK'ed because the only one being able to do reliable damage than would have been the rogue.
3/4 of the party would have been reduced to be as effective as commoners (a caster without spells is barley better at fighting than a commoner).
And so far all the parties I played in or DMed for a primarily casters/specialists and not martials.
It shouldn't. If the PCs can give it out they'd better be prepared to take it right back, especially if their foes are other adventurers (which happens now and then). I don't believe in PCs-are-special design.
I agree in principle, they shouldn't feel special in the game world. But at the same time, they are special.
Because Non-Special people who get in 1 to 7 combats a day with monsters that will rip you apart would kill any non special person quite quickly.
It is always a balance act. Like the world shouldn't level with the players, but the adventures should be achievable by the characters and not have an ancient red dragon attack a level 1 party because it would be realistic in this world.