As a class, Rogues keep up pretty well with fighters in damage. Sneak attack damage stays broadly comparable with equivalent extra attack damage, and their superior manoeuvrability and uncanny dodge help significantly in staying alive.
In your game, when two identically-dressed warriors step into the tavern, do the patrons automatically know which is the fighter and which is the bard?
Level 11 you're looking at what? +10 to hit? Unless you're still just exclusively fighting zombies at that level, almost any attack in definitely not guaranteed to hit.
Maybe thinking of it like dice might be easier for you to visualise it:
In any random situation, there will be a random level of capability that your character may be able to apply to it.
At baseline (1) you're making non-proficient ability checks on non-primary abilities. Then you might have proficient ability checks on non-primary abilities or non-proficient ability checks on primary abilities (2). Proficient primary ability checks get you 3, but if you're really lucky you may be able to apply a proficient primary ability check with some sort of special bonus or advantage to get a score of 4.
Spells allow more spectacular results than you can get with ability checks: a high-end spell directly applicable for the situation might score a 6, but lower-level, or spells not specifically designed for the situation would be lower, all the way down to not having any applicable spells for this random situation. Or being out of spell slots. - There is no guarantee that in any specific situation a caster will have the right spell.
The issue is not so much that wizards get to roll a d6 while fighters only get a d4. It is that wizards roll both a d4 and a d6, and pick the best. Even if you posit a situation where there are no spells applicable, the wizard class has the same options as the fighter class. If not better, because like all casters, wizards can be generally better overall than fighters at ability checks.
. . . and the fighter needs Strength, but may also want to put better scores into dexterity and constitution if they want to live.
Having a powerful ability but choosing not to use it all of the time is better than not having that ability at all.
OK. You specifically added the bolded words: they are not part of the original statements that you are reacting to.
Why did you feel the need to do this?