Remember that you need more fuel to do that though. It's a two-fer but not a freebee.

It's not free (especially the hardware) unless you compare to e.g. ethanol/biodiesel; with biofuels, you get less energy at the wheels and no space heat at all.

If you used the electricity in the house then you'd get all the energy as heat.

Unless the cogenerator is very inefficient or the building is very well-insulated (by today's standards), the electricity production will often exceed demand.  If you just turn it into heat, you've used a lot of hardware to do the job of a flame.

Cogeneration can produce "something from nothing".  Suppose your alternatives are a 95%-efficient furnace or a cogenerator which yields 30% as electricity, 65% as heat and 5% losses.  You can run 1/3 of the electric output through a heat pump with a CoP of 3 and have the same 95% of the fuel's energy as space heat, plus you have 20% of the fuel's energy as electricity.

If the developing solid-oxide fuel cell technology can be turned to domestic use, cogenerator efficiency could hit 50%.  A therm of gas could create 1/2 therm of heat, plus 14.64 kWh of electricity.  14.64 kWh of electricity into heat pumps achieving 3:1 (far from the best available) would produce another 1.5 therms of heat; the system would effectively double the gas supply.  Or you could settle for making up the balance of 1 therm of heat and putting 9.76 kWh of electricity into a PHEV.  At 200 Wh/mi, you'd get close to 50 miles out of that energy.  That would displace roughly a gallon (115,000 BTU, or more than 1 therm) of liquid motor fuel even in a Prius.

No, there is no magic in this.  Energy is conserved, and the efficiency figures have been demonstrated.  All it does is refuse to give in to entropy too easily.

Seems to me that you do better using wind or solar and leave the plants to themselves.

Seems to me you're not seeing the whole picture.