Alright.. bad design aye. Well, it is somewhat subjective and it could go on for an infinite length of time but I'll make some clarifications I suppose.
Let's just imagine that this game is hyper-RPS; the analogy dumbed down would be rock is attack, paper is shield and grab is scissors. If a character's capabilities are skewed in such a way that they are able to forego one part (i.e. rock) and still win, there is something wrong.
Pre-patch Diddy in comparison to now... could win with just paper and scissors as well, his entire kit that focuses around an interesting 'rock' wasn't worth developing or using at most levels of play because you just didn't need to.
Sometimes the issue is because of overtuned numbers (damage for example) which pushes risk/reward towards an inane scenario. Captain Falcon getting to 100% and switching to 'back air only' because of its safety, damage and kill power (sub 100% type of KO power) were skewed enough that Falcon could get away with this. Back air is still a good "walling" move, is still very safe on shields, but from just a 1% nerf no longer becomes a 50/50 with rewards so heavily skewed in the Falcon's favour that he could successfully pull wins playing like this. A character which has top tier specs in 'aggressive' approaching and rush down also having a near insurmountable walling tool; it didn't make sense and it resulted in an "abusive" character.
What constitutes bad design to me is the lack of universal counter play to a move or strategy.
Character specific strengths/attributes are meant to alter match ups not by hard countering or completely nullifying a tool, but rather giving an additional option among the universal options all the other characters have.
Good [dash] grabs, for the most part, have never had real counter play to them, they're a class of some of the longest ranged moves, give massive reward, beat shields, and for those strengths have excessively low risk on average (the best outspeeding defensive options in smash4).
Ice Climbers in Brawl only needed a grab for a stock, and some of the most dominant ICs played in such a way that only a few things would happen: Ice Blocks/Blizzard nullifying your zoning game and CQC (if you dared to...), dash grab to back roll only being possible to capitalize on if you could hit both climbers (hitting only one equated to death), and as being in the air countered grabs having one of the best up airs with some of the best landing coverage tools equated to a
completely dead game within a year or two of ICs being realised in this way. These tools all had very little single options that could overcome them at all... Marth and MK were the two characters in the game who could use aerials against Ice Climbers (fair/dair outranging blizzard and not being laggy enough to give a guaranteed grab if you didn't hit both climbers).
Luigi has a similar thing going for him, fireballs nullify many character's neutral games, people have to take risks/mix up to even get near him, yet he easily and generally reactively covers every possible universal choice with another fireball, a dash grab or up smash/etc. Worst case scenario he has to shield, which given his poor traction would be really good if damage values on average weren't as low in this game as they are when the range of his dash grab is A LOT longer than a majority of shield pushes would be.
In Brawl, Melee and 64 a universally good option was nerfed significantly, the amount of lag one suffers from clanking was increased, a character could jab some of the faster projectiles and usually be neutral in frame advantage if not ahead; walking and jabbing things as an approach was seen as a significantly stronger choice than walking and power shielding for most characters (MK being a character who could not do this, a reason why Marth did better in some match ups due to better approach options). If the projectile was particularly meaty or solid in CQC situations, a 50/50 interaction would occur from the clashing that was more option rich than shielding but obviously wasn't as safe as shielding.
In smash4, that 50/50 interaction is now close to 100/0, clanking with a projectile like you would in every other game is a death wish.
Without that counter play being possible, then the only characters who can get by it are those with fast start up, long ranged, low landing lag aerials (clank lag not existing on aerials), any character on the ground within Luigi's fireball and dash grab range who doesn't have Sheik's fair actually have close to zero options Luigi cannot cover multiple of with just one.
That to me is bad design. A character's kit covering nearly all universal options with a few single button presses and only CHARACTERS can stand a chance if they have a tool that's better than fireball in neutral. Overtuning is different, other characters have similar abilities just not as strong, their kits overall not requiring that extent of favourable numbers to be strong and functional. While engine changes have benefited Luigi in a way I argue is too much, the overall balance in the game of lower damage pokes and "poor" short hop games really helped Luigi to not be so naturally at a disadvantage against most characters; the latter is probably a good thing.