Usually, people do take the rest of the party's choices into consideration, but only thinking about one's own character doesn't necessarily mean that the party doesn't work together. In many games, the fact that the characters are individuals and are not made only to maximise the teamwork provides the basis for the role-playing.
In other words, making a character without the team in mind means that the team has to think about how to use their strengths and work together despite their weaknesses.
Those are the basic guidelines, but they are not required to be filled. Since the game has a DM, who controls what obstacles the party faces, a game can be made to fit the style that the players have, rather than having to fit to one particular style. If the party consist of rogues and wizards, the game may focus on intrigue and stealth, while a party with mostly fighters may focus on warfare and battle.
However, most parties still have members who can fill the roles to an extend. A rogue has the best abilities for sneaking and lock-picking, but everybody can learn those skills to a degree, for example. Considering how many games have more than four players, there will usually be someone in the team who can fill every role if they need it.
If you want to play a game that focusses on filling out the roles and balancing the team, that can certainly be done and many DMs will be happy to have such a game, however. It's just that D&D does not require anyone to stick to a predetermined model if they don't want to.
That would be because they are not made to do that. The games are not based on the characters having to have personal data that relates to each other at all. Often, the characters start as strangers, meeting for the first time and having to work together for a common goal despite not having personal data that relates them to each other. They can be related, though, and that is also a good way to play. It's just not the only way.
EDIT: Apologies for rambling about Dungeons & Dragons. m(_ _)m I didn't have much to add about your art that had not been said. They are all amazing, particularly the Legend of Zelda* ones and Lukina.
*I guess I could add that the games are named Legend of Zelda in English? Sorry! m(_ _)m