If you're going to take fuel into space (the fuel being literally 80% of a space craft's weight or more) what's the point of leaving the ignition source on the ground? Combustible fuel burns Just Fine without a laser, ignition is cheap. The same goes for nukes.
Lasers work for an air-based craft because the laser (i.e. the power source) remains on the ground and turns the ambient air (free!) into plasma, which provides thrust.
In space, there is no air. Because there is no air, you get nothing for free.
The only way you can use a ground-based laser to propel a ship through space is if the ship weighs virtually nothing and has a very large light sail. Photons DO carry a very small amount of thrust capability to them, but you need trillions upon trillions of them to get an appreciable thrust.
It's called a photonic laser thruster and it works by bouncing light between two mirrors. You can get a whopping 3.5 millinewtons with a 500 W laser. You need 5,000,000,000 newtons (roughly) to achieve escape velocity from Earth. That's 1,000,000,000,000 (one trillion) times as much power input needed which is on the scale of the most powerful laser ever built (and its still only half as much power as we'd need).