@Feliaria
I see what you're talking about, and I'm a huge fan of buffs, debuffs, and utility spells personally, but the battle system you've been describing still seems pretty "big stick, bigger stick" to me.
The goal of any combat encounter is to win. The only way to win is to deal damage. Burn effects and other Damage Over Time (DOT) effects are nice, but nevertheless it's still damage. Lowering enemy stats is good to reduce the damage they dish out to your party or increase how much damage they take from your party's attacks, but at the end of the day it's all pointless if you aren't doing any damage and the enemy kills you.
From a player perspective; "Why bother with non-damage spells/abilities? Just hit them with my biggest stick until I win". Anyone who has ever played Pokemon knows exactly what this is like - you'll have some move like Tail Whip that does no damage and you'll replace it with something like Ember or Water Gun as soon as possible. By the time you hit the Elite Four each of you're Pokemon will have either 4 attack moves or 3 attack moves and a powerful buff/debuff. And your team will probably consist entirely of "sweepers" that hit for massive damage but go down fast if they go up against the wrong type match-up, and any Pokemon focused on defense and boosting defensive stats at the expense of damage will stay in the PC. Because tanking damage but not being able to dish it out is not how you actually win.
And that's in a game with Elemental type-matching as a core focus of gameplay. If there was only generic "damage" or even a "physical/magical" split then it's even easier. Just use the skills that give the best Damage to Cost ratio - in any action-oriented combat system this is usually done in the form of an "optimal combo" and any skills not part of it don't get used. Period.
From a developer perspective; "Why bother giving the player these non-damage spells/abilities in the first place?" If the goal of combat is to win - and it is - then why bother with anything that does not immediately bring you closer to winning the battle? Is there some purpose for me making the player waste a turn dealing no damage now just to deal a little more damage later?
You need to seriously consider turn-efficiency when designing, because your players absolutely will be. Say my basic "Fight" command can hit for 100 damage and I have two abilities - one is a non-damaging poison debuff that lowers the enemy's defense and the other is a fireball spell that deals damage. This makes me think of a couple possibilities for the player:
1. The poison debuff means I use a turn doing 0 damage and my basic attack next turn deals less damage than just using the "Fight" command twice.
The poison skill is therefore useless.
2. The poison debuff means I use a turn doing 0 damage and my basic attack next turn deals more damage than if I had just used the "Fight" command twice.
The poison skill is therefore optimal and it is the best choice 100% of the time to end battles faster.
3. The fireball spell does less damage than my basic "Fight" command attack.
The fireball spell is therefore worthless and will never be used.
4. The fireball spell does more damage than my basic "Fight" command attack.
The fireball spell is therefore optimal and it is the best choice 100% of the time...provided I have the MP and if I do not have or need to conserve it then I will mash the "Fight" command while wishing I had more MP.
The main problem I see is that if there is only Physical Attack/Defense and Magical Attack/Defense, then only one kind of damage is ever needed. Ever. If an enemy has high physical defense, then I hit it with my biggest magical stick. If the enemy has high magical defense, then I hit it with my biggest regular stick. If physical damage is the most effective then why use anything besides my basic "Fight" command attack since it has no resource? If magic damage is the answer then why use anything that isn't my biggest spell, or at least the one with the best damage-to-cost ratio?
If Fireball does more damage than Icebolt, then Icebolt has no reason to exist. If both spells do the same damage then why would you ever need more than 1 of them?
Status effects and debuffs will only get you so far. As the League of Legends community says "The best CC is death". What's the point of any status effect? To lower the damage the party takes or increase the damage they deal. Paralysis, Frozen, Rooted, Stunned, Immobilized, whatever you want to call it - it only exists to stall the enemy for 1 or more turns.
But what's the point if it means dragging out the fight? Ending the fight faster by doing more damage also means your party takes less damage. There is never a reason NOT to try and end the fight as fast as you can. Since damage is the only way to actually WIN a fight, there are ultimately not many times that dragging the fight out with non-damaging status effects or delayed burn/poison damage is actually helpful.
The purpose of an "Elemental System" is so that the player has more tools that MIGHT be the correct, optimal choice. If you have the player encounter a new enemy type and they do not know what type of damage is most effective they will have an incentive to try out a wide variety of spells to find out how to take them down in the fewest number of turns. The more tools they have the longer this experimentation will take. This means they can encounter the same enemy type - or even the exact same troop composition - without getting bored since they haven't found the best strategy yet.
The player's kit and each different enemy troop composition form a puzzle, with the "answer" being the method to defeat them with as little MP as possible, or taking as little damage as possible, or in the fewest number of turns as possible. What was once a tough fight at the start of a dungeon could become a one-round stomp by the end of it, and the player can feel good for figuring out the best use of his turns to make it happen.
The biggest consideration will always be; "How long do I want my mob encounters to last?" If you, as the developer, want the player to HAVE to spend say 5 rounds fighting a specific enemy troop composition then you could force this to happen by making your random encounter enemies all tanks that require multiple rounds of status debuffs and effects to start dealing decent damage to. If you would rather have battles that end quickly then there is almost 0 point to having tons of status effects and debuffs since the player will not be using them except possibly on bosses.
Having different types of damage allows the developer to make fights artificially tougher when the player first encounters them which become much faster as the player becomes accustomed to their weaknesses and how to most effectively deal damage to them. This is extremely important as it can make new areas interesting and engaging while also making it much less tedious by the time the player is finishing up or if they have to backtrack at some point.