Power and Balance

The difficulty is keeping everything somewhat balanced. Lets choose some reasonable scenarios and examine balance of feats and fighting styles in 5e. Thinking of damage output at 3 different levels. Lets not consider the weapons and spells that aid combat further.

Level 4 assuming an 18 stat

Level 8 assuming a 20 stat and 2 regular attacks and +1 weapon

Level 12 assuming a 20 stat and 3 regular attacks and +2 weapon

Base Line Scenarios
Great Sword Wielder

4 2d6+4 = 11

8 2(2d6+6) = 26

12 3(2d6+7) = 42

Long Sword or a Long Bow (have advantage of spare hand or range)

4 1d8+4 = 8.5

8 2(1d8+6) = 21

12 3(1d8+7) = 34.5

Simply Fighting with a light weapons in both hands

Main attack is now 1d6 not 1d8, bonus action attack is 1d6 no stat bonus

4 2d6+4 = 11

8 2(1d6+6)+1d6 = 22.5

12 3(1d6+7)+1d6 = 35

Benefits of Feat or Fighting Style
The most damaging would be Polearm Master which cost a bonus action, requires a weapon that is a d10 not 2d6 (-1.5 average damage), both hands (i.e. not shield) and gains you another attack for 1d4+4 (assuming 18 stat) damage.

Also an oppourtunity attack when they enter your reach, assume that triggers 2/3 rounds

4 that is -1.5+1d4+4 + (2/3)(1d4+4) = +9.35 damage per round compared to great sword

8 -2(1.5)+1d4+6 + (2/3)(1d4+6) = +11.20 damage per round

12 -3(1.5)+1d4+7 + (2/3)(1d4+7) = +11.37 damage per round

Archery Style: +2 to hit assuming normally hitting on an 10, roughly equates to +20% more hits

4 +1.7

8 +4.2

12 +7.9

Dueling Style

+2 damage

4 +2

8 +4

12 +6

Two Weapon Fighting Style

+ Stat to off handed attack

4 +4

8 +5

12 +5

Crossbow Expert

Assume fighting with a hand crossbow (1d6) and reloading it with your spare hand, comparing it to a long bow

4 (-1) +1d6+4 = 6.5

8 2(-1)+1d6+6 = 7.5

12 3(-1)+1d6+7 = 7.5

Great Weapon Master

With a great sword, just considering the bonus attack,experience suggests it will trigger about 50% of rounds. Other ability is useful but much harder to judge its value.

4 0.5(2d6+4) = 5.5

8 0.5(2d6+6) = 6.5

12 0.5(2d6+7) = 7.0

Great Weapon Fighting

With a great sword, rerolling the 1s and 2s. Taking if off the web

4 = 1.3

8 = 2.6

12 = 3.9

Summary
The basic 4 combat techniques or 2 handed, sword and board, 2 weapons or ranged are reasonably viable. Most players prefer 2 handed as it does the most damage when you stack up a few options on it. But realistically the other options work. Sword and board is better if you consider the effect of a magical shield so the AC bonus is much Higher (+2 for a normal shield, +5 for a +3 magic shield) or if you want to do something like use the shield master feat. Ranged always requires the right scenario and is probably the weakest in general.

The problem. The combat effectiveness of the options vary wildy. Not really balanced at all.

Some weapons like certain polearms and hand crossbows get a great option, most weapons have nothing much.

I don't demand everything is the same, cookie cutter design is just lazy. I perfer real variety. I do think there should be good options for most weapons and fighting techniques.

In order to keep everything reasonably balanced my yard stick will be to make sure none of the options gets more powerful that an optimised polearm fighter, which seems to be the top end of 5e combat. Hence an option that gives a reliable attack as a bonus action, or on a reliable trigger is probably too strong. Perhaps 50% is alright or the option must have some other cost.