For fun, here's the math if Paladin and Barbarian actually get 3 attacks instead of being stuck with only 2, and use +4 weapons as I suggest.
Baseline:
Fighter 75.2
Paladin 71.4
Barbarian 75.9
Wow look they actually compete with each other again, who would have thought
Let's try this then
A Fighter, a Paladin, and a Barbarian walk into a bar. They all have GWM and PAM as the optimized 5e build, with +3 weapons even though both DMGs tell DMs to give their players +4.
The three agree to a contest of arms attacking a training dummy to see who has the highest...
Once again, this relies on some assumptions: the Barbarian Reckless attacking two rounds every combat on average for example. The Paladin saving their Smite for a critical hit half the time is another. And while published adventures tend to be generous with loot, it is ultimately DM fiat over...
An easy way to prove this is as such: how much added damage does a single weapon Feat grant in 5e? They all perform remarkably similarly, because the Fighting Styles make them all perform the same.
If that level of numerical care was taken with the Fighting Style+Associated Feat combo, then it...
Paladin smites are equivalent-ish to Fighter action surge, and Barbarian's added rage damage + other rage benefits.
No, a paladin with 2 attacks at level 20 is not equivalent to a Fighter with 4. For every "cast a spell" there's an equivalent action surge of 8-9 attacks in a single round nova...
What is stopping you from being part Lich, part Death Knight, and part Ooze Lord all at once? The chains being psuedo-class identities is strange. Ah yes, I am a Death Knight Gish, but my main class is Barbarian
There is a problem that simply by labeling and dividing them up like this, we imply each type can only do its own thing. Which is incorrect.
IMO each style is about the order of priorities, and I thank you for pointing that out. Every edition had each of these as somewhat of a goal, it is...
TL;DR Theater is the type of group that yaps for three hours and then have a single combat per session. I do not think the game focus is the only reason this happens, famously 3.5 had a similar problem caused by combat length after all, but Theater generally assumes risky moments might happen...
Player improvisation can happen no matter which paradigm the game is under. It's about level of scale and impact.
You mention the classic examples of flooding the dungeon, but I can counterpoint with a classic example of player improvisation in combat as sport: swinging on a chandelier across...
Arguably 5e brought around the Theater school of thought by using Inspiration as a baked-in metacurrency to focus play on more than just monster bashing. The new school games that came after 5e, like Draw Steel and Daggerheart, embraced using metacurrencies to push the game in a direction they...
Playing the world means the level of gameplay decisions that affect combat are at the macro level, not player build vs monster manual level.
Combat as sport puts the onus of handling combat on player build and party build. Combat as war puts the onus on decision making. Negotiate, fight...
Daggerheart literally has a system for sharing the spotlight, or focusing on one character as they get their power moment. 5e tells GMs to fudge rolls to make the story interesting. The style is indeed about mechanics, and deserves to be among the other two
While seemingly about combat, each descriptor more describes what the relationship between combat and the rest of the game rules is. Or what the game wants out of combat in its system.
War sees combat as flashy, but ultimately an obstacle to be interacted with. Talk, fight or flee, each has...