"Rockets require an enormous amount of fossil fuel to get into space."
Although some smaller devices for separation and guidance used solid fuel, only the first stage of the Saturn V vehicles which launched the Apollo Missions used masses of Fossil Fuel. Stages 2 and 3 used Liquid Hydrogen as the propellant. I think the first stage got through about 2,000 tons of fuel but this included the liquid oxygen required to make it burn. So say about 1,000 tons of Liquid Rocket Fuel required. This is about 2.5 million gallons. The USA consumes getting on for 400 millions of petrol and diesel a day, so perhaps the odd mission to the moon will not see the pumps run dry. Of course energy is required to produce Liquid Hydrogen and Oxygen, but once again compared to the energy consumed for other purposes, the amount must be trivial.
I think this scheme is a good idea simply, as jim says, "because it's there". The trouble I foresee is not so much with the amount of fuel required but more with the enormous sums of cash it will consume. I remember "Project Apollo" very well and there were huge protests in the USA about the amount of money being used to fund it when the USA had social problems that required cash. It was cash that caused the programme to be curtailed and the final three missions were cancelled. The other problem is that few people would envisage any benefits from it. Even if it was a forerunner to mission to Mars many people will simply say "So what?" But a return to the heady days of the late 1960s and early 70s, watching a giant rocket blast off from Cape Canveral would be quite something.
BTW - I knew someone was pulling my plonker about the velcro !! :-)