Players are a big share of the game, and rules help them to create the character they want to play, and it's up to the DM to present the level of challenge desired.Characters are a big share of the game, and rules that help bring them to life are much more important than rules that only help reduce the challenge.
No character should start with any score higher than 7 with the rate of ability score increases in 5th Edition. It would stop the jealousy of other players who rolled well, and get everyone experience playing with low scores. I recommend it for everyone who plays 5th Edition.
Well, there is the artificial challenge boost you wanted, I guess. I know I would be thrilled to start with sub average scores in every single stat!

Just as magic items in 5th can break bounded accuracy, so too can universally subpar statistics. A large percentage of attacks are going to miss if everyone is rocking -2 penalties to attack instead of +2 or +3 from stats.
That's not terrible design. It's not even a punishment. It's just part of the game. Is it "punishment" when somebody in Monopoly rolls a 2 on their very first move and winds up behind everyone else? Nonsense. It's just part of the game. Your next character will be completely different.
As Hussar said earlier, this is a false analogy. It would be more like "Let's play monopoly! roll this dice. Oh! sorry, you didn't roll well.. you only get to start with only $500. Also, because you didn't meet our standards, you also cannot buy utilities or railroads" Better luck next time! - Except next time is potentially months of play down the road.
The bard seems the least well balanced class in 5th Edition PHB, being able to cast any wizard spell and also healing spells.
The bards power level is in line with the other classes in 5th edition. (finally)
It's how it's supposed to be.
To you. You mentioned earlier that "everything" feels overpowered.. this is not possible. Within context of the system, if "everything" is overpowered, NOTHING is.
You come from the oldschool systems where *Everything is Awful* (punishing mechanics, grossly imbalanced classes, forced drawbacks) 5th edition has really changed to *Everything is Awesome* (all classes are powerful and appealing, forgiving mechanics, drawbacks by choice).