To get a Keyblade, you need to be marked by a Keyblade wielder as a successor before that.
Riku and Kairi were marked by Terra and Aqua respectively. Riku was rejected by the Keyblade because his heart gave into darkness, and thgoats different than being in control of the Darkness as Darkness is much harder to control. Now, Sora had Ven's heart within him. Ben was a Keyblade wielder before and because of him Sora can use a Keyblade, and he's also the reason why Roxas looks nothing like Sora - he actually has Ven's heart, because when Sora released Kairi's heart from within him, Ven's also went free. So Roxas is technically Ven without his memories. This'll make more sense once you get to Birth By Sleep, and I hope you played Chain of Memories, because some concepts get tricky otherwise
As for why everyone has Keyblades now, you want the Wattsonian or Doylian explanation?
The Wattsonian explanation would say that at the start of Sora's journey the Keyblade Masters had been long lost and the world was in darkness, so they're kinda like the Jedi in a New Hope, and after Sora wins against Ansem, there is more light, more Keyblade wielders, yay.
As for the Doylian explanation - KH was created first as a standalone game, and after that it universe got expanded. Hence the first game is simplistic compared to the rest - it's what happens with series like this, you can't really stop the change