I don't want to speak for every fan of class balance, but I don't think anybody is seriously asking for classes to be equally capable in all situations.
Well, to be fair, 4e did try to ensure that all classes would be equally capable in combat, although different classes were intended to contribute to the successful resolution of a combat encounter in different ways. The skill challenge system was also intended to provide all classes with broader mechanical scope to contribute to the successful resolution of non-combat challenges, although the fact that different classes had varying numbers and types of trained skills already meant that here, at least, they were on a more unequal footing. Of course, contributing outside of the rules is, almost by definition, something that no mechanics can ensure, and that is entirely dependant on player creativity and enthusiasm.
However, and IMO, characters being able to contribute equally in all situations is not a problem. The problem is distinctiveness. If a rogue can open a door by picking a lock, a wizard can open it with a knock spell, and a fighter can simply break it down with brute strength, you could make an argument that although various methods are used, it makes no effective difference whether you play a rogue, a wizard or a fighter. A related point could be something that, for want of a better term, I will call the "natural spotlight". It's the idea that different characters are supposed to be good at different things, and over the course of a typical campaign, different challenges would be encountered and different characters would take turns to share the spotlight: the rogue for stealth and infiltration, the wizard for lore and knowledge, and the fighter for combat.
Now, as with equal contributions, the natural spotlight is not in itself a bad thing, and in fact, it aligns nicely with the inherent tropes of a class-based role-playing game. However, taken to extremes, the potential problem is lack of participation. If there are parts of the game where only one type of character can make any meaningful contribution, you are effectively locking out participation from players of other character types (barring, of course, contributions outside of the rules which are player-dependant, as mentioned above). You can mitigate the problem by keeping such challenges short and expecting the non-participating players to show patience, but IMO, this is tackling the symptom, not the problem itself.
There is a third issue that tends to be brought up in relation to PC contributions, and that is spotlight stealing, but I consider that more of a balance issue than one directly to do with contribution, so I mention it only for the sake of completeness and will not go further into it.
My sense of the 5e approach to contribution is that it will address the participation issue by ensuring that all classes have a basic level of competence in what the designers have identified as the three pillars of combat, exploration and interaction. It will also address the distinctiveness issue by ensuring that different classes will have different levels of competence beyond the basic in the three pillars. So, it seems to me that the designers have already recognized the two problems mentioned above and are taking steps to avoid them.
