It has nothing to do with current capacity. Nuclear has lost a lot to debates much like this one; however, if we wanted the capacity, nuclear would step up and fill it in at a reasonable price. The same amount of power generated by the alternatives would be astronomically expensive. That's one of the problems that plague the alternatives you've named: either they are far too expensive to use at any kind of large scale, or suitable locations are in thin supply, or power output fluctuates unsuitably with a change in weather, and so on. They just can't compete.
The current research into nuclear is making it even cheaper and safer (thorium, etc); the current research into the alternatives is making them cheap enough to be possible with significant demand.