First of all a DJ should have some competence with electronics. It might only be for connecting things with wires but there is that base competence. And mostly a DJ should be competent enough that they don’t manage to electrocute themselves.
Some think that the successful DJ must have impeccable taste in music. This is unfair to the DJ. In most cases they must have middling or average tastes in newer music. They are after all trying to appeal to the mass.
DJs should be able to make smooth transitions between songs. In earlier days all this meant was that the DJ needed a slider between two music players to fade out the old music and fade in the new. Today it also involves having a speed control on the two pieces of music so they can beat match as well. For bonus points the finer DJ can key match as well as beat match.
That last transition is very rarely done because beat matching has a direct correlation with speed just as pitch does. The majority of the time the needs of each will be different making a match with both almost impossible.
When the successful DJ writes a song they don’t become a musician. They instead stay as a DJ. This has nothing to do with the talent and more to do with the gobs of money DJs of today make compared to a musician.
A successful DJ will never take a request from a customer unless the DJ has designs on that customer. As an example, the DJ might have played the requested song just last week. The listener heard that and wants to relive that moment. So they request that song. The DJ will just nod at the customer and never play that song again. That’s because once the public asks for it by name, then it becomes an oldie which the successful DJ will not play again. After all the DJ has five more newer songs to replace that oldie and is dying to try them.