Why use lasers for intense, localized heat instead of some other light source?
If you want to make a small very-hot spot, spatial coherence is important. Contrary to what you say, the sun has quite high spatial coherence (not as high as a laser, but higher than most other bright light sources). That's why you can focus sunlight very well. If you focus sunlight perfectly, you get a spot the shape of the sun. That spot would have the same light intensity as if you were standing on the surface of the sun, looking down.
If you perfectly focus the light from an incandescent light bulb, you can get a spot shaped like the tungsten filament. That spot would have the same light intensity as if you were a tiny person standing on the surface of the tungsten filament, looking down. (This intensity is much lower than the the sun's).
An extreme example of low spatial coherence is the blue light from the blue sky. You cannot use a lens to focus that light into a bright blue spot on the ground. Try it! This blue light has almost no spatial coherence, which means you cannot focus it. There is plenty of blue light coming at you, but it already has as much intensity as it is capable of having.
This is quantified by the law of conservation of etendue. Light starts out with a certain radiant intensity, and then it can never be increased, no matter what kind of lenses or mirrors you use.
Lasers can have far higher radiant intensity than any other light source. It's not just how many watts they emit, it's how they emit it -- with high spatial coherence, which means it can be focused very effectively.
Lasers come in all shapes and sizes, and intensities, and wavelengths, and form-factors, and prices. Red diode lasers cost a few cents each. Other lasers cost $100,000 or more. Lasers are basically a generic way to create coherent (and therefore high-radiant-intensity) light, in many different systems. So if you need a high-radiant-intensity light source, the best one for the job is quite likely to be a laser.
The spatial coherence from the source to the needed location allows the use of more compact, lighter weight optics, and makes it relatively easy to take the light from a very bright source and bring it to the target.
If you require 5W of heating at a spot smaller than a mm square, you would need to bring the 5W incoherent light source near the target, and use a series or lenses much larger than the target to bring the light to the target. If you instead need to move 5kW of light that far, you're going to have that much more difficult a problem.
But let's say the target can't be close to the source. Since the light isn't coherent you get to use a series or mirrors and lenses that are very large, or you have to use very, very many of them, in order to contain the light in the desired path.
By comparison, the low natural divergence of the laser is very easy to move and control with relatively small mirrors and optics, and is easy to focus down to an area much smaller than 1mm square if needed.