Of course alternatives to fossil fuels cost more than fossil fuels do, provided you neglect the environmental impact of fossil fuels. If this were not the case, the other sources of power would already be dominant.
Unfortunately, the marketplace as presently constituted does not adequately account for the damage due to fossil fuels.
The fact that carbon is not already largely phased out is a simple example of the tragedy of the commons. In the global aggregate, fossil fuel use is much more expensive than it appears. It's just that you are extracting wealth from a common pool every time you use them, rather than from your own resources. The commons is the climate system. So each of us, when we maximize individual utility in our energy decisions, reduce the viability of the world as a whole, by extracting value from the climate resource held in common.
The simplest solution is to increase the cost to the consumer of carbon emissions to the point where these externalities are accounted for, and wait for alternatives to emerge from private enterprise. Since it would be counterproductive to increase the profits of the producer, this amounts to a tax. Public revenues can be held constant, if so desired, by reducing other taxes.
The devil is in the details of course, but the big picture is really not all that complicated.