[Death Note theory] What happens after the users of the Death Note die?

This actually interested me from the very start of the series since Ryuk said that when the users of the Death Note die they go to nor heaven, nor hell. And as we know that means heaven and hell exists because of this sentence. Now we know that in the anime there is a heaven and there is a hell.

But since the users of the Death Note don't go to neither we can presume that in actuality the users of the Death Note go to the shinigami realm(translation - Death god realm), from which Ryuk came in the first place. I think so, because that is the only other place mentioned that somehow maybe connected to actual heaven and hell. I'll also agree to either a fanfic or my imagination most likely that after Light went to the shinigami realm he becomes a shinigami.

The reason I doubt this is simple; Shinigami's can become immortal by killing people, which means that they most likely won't decrease in numbers except for the few if not only exception of the ones in the series. Therefore everytime a new Shinigami comes into excistence because someone used a Death Note the population would increase permanantly. This would cause them to see loosing a Death Note as a far more serious crime than they did now (or they would at least act more on it), since it potentially generates new Shinigami's which will have to kill people to stay alive. Since that is something all Shinigami's have to do they will increase the amount of competition for themselves if they let other humans become Shinigami's.