Honestly, it depends.
Ideally, it shouldn't matter what sort of character a player has, unless it goes against the campaigns restrictions (i.e., no evil PCs, no drow, no divine spellcasters, all-aquatic PC races only, etc.).
However, a party's effectiveness/survivability can be somewhat affected if they are not a "standard" group of adventures playing in a "standard" module or campaign. The two do not mix well. For example, during the days of 2nd ed. (w/ Skills & Powers), my gaming group went through Night Below, a uber-module more or less designed for an average party to go through. However, the players pretty much made up anything but a typical party--the group mainly consisted of elves, mages, & thieves, with very few non-elves (or non-unique, worthy-of-a-LA-in-3.X-mechanics), and very few actual divine spellcasters or heavy fighters. We did poorly overall in the module, and we were glad just to get the game over rather than feeling any level of accomplishment.
To some degree, it is a matter of what the players want to play (character- & game- wise) and what the DM wants to run (game-wise). If the two aren't the same, it's bound to cause problems.
Now, despite the character issues about individual fun vs. party needs, I think one of the big things that should be focused on is individual fun vs. group fun. A player is a problem when they try to have fun for themselves, esp. if their notion of "fun" disrupts the game or ruins the enjoyment for other players. As long is this issue isn't a problem, then characters really shouldn't be that much of an issue, for the most part. Hirelings & other NPCs could cover this role.
However, if the PCs (of at least 4-5+ members) need more than 1-2 hirelings to be able to successfully complete an adventure because their PCs cannot perform the necessary abilities to do so, then I'd definitely say that there was a problem with the group of PCs.
As long as the DM accounts for it, a focused or atypical group of PCs can have a good long campaign (such as a party full of elf rogue/wizards, or a party with no primary, 0-9 spell level list sort of spellcasters). But, that's if the DM accounts for it & runs adventures appropriate for that sort of party. Otherwise, I'd consider it a wise practice to have as diverse of a group as possible that at least covered most of the bases (healing, arcane firepower, combat/feats, skills, etc.; overall, the PCs should have someone who fits the role of a strong PC, a tough PC, an agile PC, a smart PC, a wise PC, and a personable PC; a good melee combatant and a good ranged combatant; at least 1 PC should have a good Will save, another should have a good Ref save, and another should have a good Fort save, so at least 1 person may be less injured/still standing after a mass attack that uses such saves; at least 1 PC with a good AC while flat-footed & 1 with a good touch AC; there should be at least 1 psychic character if it's a psychic campaign; etc.). It's possible to cover all of these bases, but it's just a matter of having the right mix of these elements (a fighter w/ high Str & Con would be good in combat, able to bear wearing heavy armor [and thus have a good flat-footed AC regardless], and have decent hit points & a fairly good Fort save; a high-Dex rogue would have a great Ref save and touch-based AC, be great at ranged combat, as well as Finesse-based melee, and would have a wealth of skills available {and a decent helping of skill points] to develop for scouting, dungeon-delving, spying, etc.). IMHO, a good group of PCs has a good mix of strengths--where one PC is weak or limited, another is mighty or capable. It sorta works in a sort of rock-paper-scissors sorta way. A bunch of high-Dex characters can be made less effective if they're either caught flat-footed or immobilized somehow (ala web, hold person, tanglefoot bags, or other movement-restricting magics/traps); if they have poor Will or Fort saves, then attacks that work on those kinds of saves can prove devastating.
So, to pretty much sum things up, it shouldn't matter with the player plays. However, it is a responsibility of the DM to at least provide fair warning of what kind of campaign he/she is running, or to at least adjust the campaign to ensure that (a) the campaign isn't a cakewalk, or (b) it isn't an eventual TPK.