[MENTION=2525]Mistwell[/MENTION] I think you are overestimating the value of a single feat. A bonus feat at level 6 amounts to little more than +1 to attack and damage rolls. At 6th level the fighter will have 18 Strength and Great Weapon Master while the paladin will have 16 Strength and Great Weapon Master. The +1 to attack and damage rolls doesn't really compete with +Charisma to all saves for the paladin and his allies, utility spells, and smite spells.
Sure many class features aren't better than a feat, but many class features are. The UA ranger's dash as a bonus action, monks fast movement and stunning fist, blackguards charisma to damage dealt, UA blade pact invocations, rogues cunning action, barbarians rage and reckless attack, paladin smites, and so on. Overall, the fighter class doesn't come with all that many potent class features on his own.
Compare the fighter and barbarian at 8th level for example. The fighter has a feat, a fighting style, and action surge. The barbarian has +10 foot speed, 4 rages per day, reckless attack, advantage to Dex saves, advantage on initiative rolls and the ability to be immune to surprise. So while the fighter can take the mobile feat to match the barbarian's mobility, or the alert feat to match the barbarians immunity to surprise and bonus to initiative, the fighter only has one bonus feat so can't match the barbarian in both. Furthermore, the level 8 fighter cannot match the durability of the barbarian, nor can he match the damage of the barbarian, even if he uses his bonus feat to try and shore up one of those areas.