It seems only common sense not to "put all our energy eggs in one basket." What if the one we bet on goes sour? But there's more to this question than meets the eye. Let's look into it.
First, we don't have to worry about any one or two energy sources taking over. Even if everything favored one source, it is not possible for any one or two energy sources to take over the market. Each is constrained by its own particular limitations, so we are not going to see any near-future domination of the energy field.
Nuclear is the one source in a position to greatly expand its production. Between 1970 and 1990, the U.S. built about 100 new nuclear plants. We could build another hundred in the next 20 years, and there is a bill in the Congress to do just that. That would raise nuclear's share of the market from 20% to 40%. It would still be outranked by coal at 50% or more.
There are many obstacles to doubling nuclear, but there are no technological questions or uncertainties. That has been proven, year after year, over the past several decades. No other energy option is even close. We could double wind or solar or biofuel, but that would be doubling only a very small output. The doubled electrical output would still be trivial.
There is another factor, fundamental but often overlooked or dismissed, We are used to comparing things that are all about the same order of magnitude. All combustion fuels, from gasoline to switchgrass, have about the same energy density per pound, within an order of magnitude. These we can reasonably compare.
All commercial aircraft have about the same cruising speed. But if you offer to supplement an airline's fleet with trains, you'd get some complaints. The cruising speeds of trains and planes are only one order of magnitude apart, perhaps 55 mph vs, 550. Suppose, for the sake of diversity, you also supplied some skateboards--another order of magnitude less. You'd get some pretty strong objections, saying that these "substitutes" are not even in the same class as airplanes.
In this context, recognize that any nuclear process is at least ten million times more energy dense than any non-nuclear process like combustion. And solar or wind sources are even more dilute, as well as being unpredictable. Nuclear is in a class by itself.
So, even if the uncertainties and problems of other fuel sources are eventually solved, we have to ask: wouldn't it be easier to just build another nuclear plant? That's something we've proved we know how to do. Nothing else is in that position.