Maybe I've missed something, but as far as I am aware, there are only three ways to interrupt spells in 5e.
Yes, in fact you missed two ways to disrupt a caster, both of these normally happen as actions on your (the disrupters) turn.
1. The first is covered under Ready on page 193 of the PHB. If a caster has readied a spell you can attempt to disrupt it by breaking his concentration before the trigger occurs.
2. The second is on page 202 of the PHB under Longer Casting Times. Any time a caster is casting a spell with a longer casting time than 1 action you can dirupt it by breaking concentration.
The underlying question in the original post is not "CAN a martial character interrupt spellcasting" - the OP concludes the RAW do not support that in 5e - but rather "SHOULD a martial character be able to interrupt spellcasting."
But the rules do support it.
ECMO3, my sense is that you have already made up your mind about the conclusion you would like to reach ("casters should be uninterruptable") and are ignoring all arguments to the contrary, because you are not actually addressing the lines of reasoning people are using to come to a "yes they should" conclusion.
Absolutely not. You gave examples of how they already are able to be interupted, and I gave you two more.
ARGUMENT IN FAVOR BASED ON GAME BALANCE (VERBOSE AS I DON'T THINK ECMO3 HAS ENGAGED IT YET - APOLOGIES IF HE HAS AND I MISSED IT BUT I'M PUTTING THIS HERE BECAUSE I HAVEN'T SEEN THE WHOLE THING ARTICULATED START TO FINISH)
Observation 1: Spellcasters have access to many spells capable of rendering martial characters unable to utilize their abilities in a single action (casting the spell).
Observation 2: Martials have access to only one method of rendering casters unable to utilize their abilities ("reducing HP to zero") which can only succeed with a single action in very limited circumstances ("caster HP lower than martial's single-action damage-dealing capacity").
Obvservation 3: Casters also have access to many spells capable of rendering other casters unable to utilize their abilities in a single action (Feeblemind, Hold Person, etc.).
Observation 4: Martials also have access to only one method of rendering other martials unable to utilize their abilities (reduce HP to zero) which can only succeed with a single action in very limited circumstances (and these circumstances are less likely to be true for martial targets than caster targets (martials usually have better AC and HP and thus are both less likely to be hit and less likely to have HP lower than the attacker's single-action damage-dealing capacity).
Any discussion on balance must consider the level and the specific classes. At early levels optimized martials are more powerful than most optimized casters through the first two levels (except Druids and Clerics) and depending on specific classes we are comparing at some martial classes are ahead of some full casters classes beyond level 10.
So if we are going to do this based on balance, it should be a thing for some casters, at some levels, but not a thing for them at other level. Making it easier to disrupt all casters would make the game MORE unbalanced at lower levels.
This prevents a real problem for both immersion and game design; to really balance the game we would need to make it so a 9th level Wizard casting a 1st level Magic Missile can be interrupted by the goblin standing next to her, while a 1st level Wizard not only can't be interrupted casting the same spell but also gets an extra dice for damage to "balance" the game and make up for the fact she is weaker than the Monk in the party.
Meanwhile the 1st level Cleric should get disrupted as it is the most powerful class at 1st level, and should continue to get disrupted until level 14, when all of a sudden an optimized Monk is more powerful than she is .... but wait the fighter is not more powerful than her so maybe she should still be disrupted?
That said the observations you make above are not really true.
Observation 1 and Observation 3 "Casters have access to many spells ...." A first level Sorcerer has access to two level spells total (3 with certain subclasses), so this statement is patently false for a 1st level Sorcerer and mostly false for a lot of other casters (virtually all of them at 1st and 2nd level).
Observation 2 and Observation 4: Martials have more than one method of making casters unable touse abilities. Improvise an action is available to all classes and can be used to prevent casters from using their abilities (both spells and others) or other martials from using their abilities. Further the disarm action can severely gimp another martial, especially since you can pick up his weapon off the ground. Finally, many other things doable by martials using equipment available. A net for example can be used to restrain an opponent an unlimited number of times a day.
Conclusion 1: Based on Observations 1 and 3 and Premise 1, Caster vs. Caster interactions are balanced.
Conclusion 2: Based on Observations 2 and 4 and Premise 1, Martial vs. Martial interactions are balanced.
Conclusion 3: Based on Observations 1 and 2 and Premise 1, Caster vs. Martial interactions are NOT balanced.
Conclusion 4: Based on Conclusion 3, the rules as written provide for power imbalance between Casters and Martials and are therefore unsatisfactory if a balanced game is desired.
Even though the observations are generally false, these conclusions are true at certain levels but they are untrue at other levels.