Don't forget that there will also be alot of overlap. Some characters are going to have some skills in common. You might have two party members that have spot, or diplomacy, or whatever else. That reduces the total number of skills that the party covers.
Yes, I mentioned this also, but... I know I'm going to say something that will make people object vehemently, but I really think that this overlapping should be discouraged (by DM and guidelines in books, not hard-discouraged by the rules) or at least it should be pointed out that having different PCs good at different things is
better for the game dynamics.
Two PCs with good Diplomacy scores is going to cause more problems than benefits. The benefits are mechanical (two PCs able to try the same check normally means the party has better chances at winning it) but the problems are social i.e. for gameplay dynamics: you can easily get one player frustrated because he has invested in Diplomacy (or whatever skill) but another PC is even better and gets to use it all the time.
The problem is indeed a very high-level cultural problem with players, that most of the time "build" their characters in a vacuum, "optimizing" their PC without thinking about the rest of the party. This is very common in 3ed, and always leads to player thinking they absolutely need this and that or their PC will be too weak, because really they keep thinking as if their PC will have to be capable of defending against everything, as if they were playing
alone. It's a general problem, more related to defensive capabilities (getting high AC, HP, immunities/resistances, defensive spells, action points/second winds mechanics, healing, defensive spells and magic items, Initiative, Listen & Spot...) but also affects skills. This tendency of players at approaching PC design as if they should handle anything without the need of the rest of the party, is what makes gamers demand more and more stuff on their character sheet at every edition and at every gaming table... Just notice what happened to healing in D&D! Since 4ed everybody now pretty much demand to be able to heal himself.
I still have a different view on the game, that a D&D adventure is played by the
party of PCs, and that this is a very major point in playing a
roleplay game, where everybody has a
role, and is not "always equally good all the time at everything".
Thus going back to skills specifically, this means that IMHO it is a
good thing if there is only one PC good at Diplomacy, only one good at Kn:Arcana, only one good at Search, only one good at Survival...
Then when you need Survival, there is
one PC getting the spotlight, not two sharing it in a way that most of the time means one of them handles it and the other tries only if the first failed.
Some skills like Listen & Spot are useful on an individual basis, particularly to avoid being surprised. I have issues with these as well, but unfortunately I haven't found a way to deal with this problem, and it's not even related to multiple PCs having the skill
bonus but more fundamentally related to all PCs being
able at trying the check. As soon as the players figure out that ALL of them might be entitled to a Listen or Survival or Diplomacy etc check, they will all try (unles there's a penalty for failure)... when you have 4 people rolling, it becomes highly unlikely that all will fail, and this will require the DM to rethink all the DCs in order to reinstate reasonably interested chances for success/failure. Net result? Lots of rolling for basically the same outcome, and less emphasis on the character who actually invested in such skills.