For the same reason that the Niners coveted SJ so much: more of the Giants' ticket holders are in the south bay as are in San Francisco. There is a lot more disposable cash down here than there is up there.
Not even. Even though it was designed as a multipurpose venue, it was specifically created as a home for the Raiders, who were at the time playing in 22,000 seat Frank Youell Field (below).
The condition for the Raiders not moving away in the early 60s was the now familiar refrain of "build us something better". What they got was, at the time, one of the best football fields in the country. As you can see below (pic taken just after the complex opened in 1966) the football field was shoehorned in quite nicely, even though the permanent part of the seating was basically a circle. 54,000 chair seats, and all close to the action. The Raiders had their fancy home, Oakland now felt it belonged on the map, and everyone was happy (except the Niners and San Francisco, but that's another story).
The sharp-eyed among you will notice that they hadn't even bother to plant grass in what would be the baseball outfield. That's because there was no actual team on the horizon. That changed in late 1967, when an assistant to Charles O. Finley, owner of the Kansas City A's (basically "Athletics" was completely dropped while he owned the team) paid a visit. The assistant said 'this is nice, can you do baseball?', and Oakland said 'sure, we can do baseball, look at these plans', and the deal was struck. The Raiders were slightly less than overjoyed, but a rent reduction shut them up. The A's moved to Oakland for the 1968 season.
But the problem with the baseball layout has always been the huge amount of foul territory, and how many of the fans are a long distance from the action. For a long time the A's made the best with what they had, but when the Raiders came back, and they built Mt. Davis to accommodate them, the relationship between the A's and the Coliseum management soured, and has remained sour.