I think it's less a matter of being biased against "front-liners" as it is being biased toward caster-types--that may be me splitting hairs, but I really do mean that. That is, I think the balancing act forced by having to consider three physical stats for different purposes is probably a good thing in the long run, and that it is the SAD-ness of pure-caster classes that makes them a problem.
4e "solved" this problem (for a given definition of "solved," anyway) with two or perhaps three things. The first: rejiggering stat priorities as a class subclass* feature. Dragon Sorcerers get, as a feature, +Str to AC--which keeps them on par with Chaos and Storm Sorcerers, who rely on Dex as their secondary stat (all of them rely on Charisma as their primary stat). Second: Once the designers realized that "A-shaped" classes (one core stat which could choose one of two, or more, secondary stats) were a better design choice than "V-shaped" classes (choice of two core stats, a single secondary stat for everyone), they worked to make sure that every class worked that way--by the end, Wizards could use anything but Strength as a secondary stat IIRC (and Staff Wizards, who used Con, were beefy and Defender-like!), while Fighters could use anything but Int or Cha. The possible third that I'm unsure about: the switch from saves to defenses and, thus, the possibility of varied/mixed attack stats. Unlike a magic-uses-saves system, where inherently one stat boosts (nearly) all combat spell effectiveness, everything-is-attacks means that you cannot do well with every spell you could pick up; you can't mix and match the very best options because you aren't guaranteed that you're equally proficient with them. (Build-specific power features, e.g. "Power X: Effect Y. If you're a Staff Wizard, add/substitute improved effect Z," also contribute to this: subclass features like this meant you could choose anything, but had an incentive not to "play against type" as it were.)
13th Age, a similar but definitely different game, goes in a very different direction. While some things are still based on one stat, e.g. Con for HP and Dex for Init, most of your important derived stats (AC, Phys Defense, Mental Defense--PD/MD are 13A's equivalent of 4e's Defenses) depend on the middle (technically median) of three stats. For AC, Con/Dex/Wis; PD is Str/Con/Dex; MD is Int/Wis/Cha. If two are the same, one of them . This rule acts as a counterbalance to the "pump your core stat as high as possible" ethos: sure, you can have sky-high Str as a Fighter or Int as a Wizard, and you'll hit more and do noticeably more damage, especially once the tier multipliers come into play. You'll also have substantially lower defenses than a more well-rounded character, and get (slightly) less benefit out of the Escalation Die (which only boosts attack, not damage or defense). There's also the 13A Background system, which is explicitly as flexible as the most flexible version of 5e skills: any Background can apply to any ability check if it makes sense--e.g. "Retired Legionnaire" can be used for Cha to persuade a fellow former soldier, or Int to deduce the goals of a confusing set of enemy marching orders. This still means high Charisma is worthwhile if you want to do persuasive things (etc. for the other stats), but you can easily get almost as good a benefit just from having a solid background--and not being able to apply your background can hurt more than a good stat helps.
So I think the problem for 5e is just that it has allowed too much to remain single-attribute-dependent for casters specifically. Probably the only way to "keep it D&D" while fixing this would be to fork apart certain elements of the casting paradigm and make them universal across all casting classes. E.g. Intelligence is always the stat for getting bonus prepared spells, because Intelligence is the stat that covers memory and reasoning; Charisma is always the stat for save DCs because it judges how strong your force of personality is for making your magic "stick" to someone. Not sure what you'd do with Wisdom though; a few options come to mind but none are quite as...clear and compelling as those first two: Wis as the magic-detection stat; Wis to defend against having your concentration broken; Wis as a bonus of some kind to buffing spells. Something like that could easily work. Then every full caster is facing a similar division of choices to the melee guys: sure, you can be a Wizard with sky-high Int, and that will be great for knowledge skills, but your save DCs will suck and you won't have whatever Wis offers. Of course, such moves would simply put classes like the Paladin even deeper into MADness...so perhaps some mixture of the solutions used in 4e and 13A would be needed.
Regardless: I think it's a matter of giving, not denying, perks. Melee guys are fine on this particular axis; it's the casters that are out of whack. Calling it a bias against melee chars implies that the casters' situation is the "default" or "proper" way to do things, and I think it's the other way around.
*The 4e term "build" is effectively equivalent to the 5e term "subclass" for nearly all classes--especially since Essentials brought in specific, slightly-more-divergent builds explicitly called Subclasses. The "original" Paladin is one of the few exceptions, not having any build-specific features, but even that is nuanced because the Paladin was also IIRC the only "V-shaped" class in PHB1, giving an effective subclass choice (do you rely on might or fervor?), which aligns with the suggested option packages--aka "builds."