Why use it this way? 3 reasons.
1. cost - it's dirt cheap compared to equivalent camcorders, and there is a very wide selection of lenses and accessories. Not as well optimized for the needs of moving pictures as other lenses (which have fewer glass elements but are easier to focus thanks to the way they are constructed) but nowhere near as expensive either. for perspective, a set of cine primes (fixed focal length lenses built for film use with industry-standard mounting connectors) can cost $250,000...or more. you can buy/rent and insure good quality still lenses for vastly less, and the disadvantages they impose are not all that serious.
2. Portability. a small indie film crew is 10 people and the camera is very obvious. A small crew shooting with a DSLR and an audio recorder can be as few as 3 people, which means you can shoot a scene in the middle of a busy street without attracting much attention. It is just so much more convenient, and saves even more money and time. the only downside to this is the ego sacrifice required to give up a big important-looking camera and the support staff required to babysit it. Instead you can just get a few of these things and shoot from multiple angles simultaneously which is an absolute godsend for editors, actors, producers, etc. Industry folk do love their high-tech gear but until recently things were at a pitch where the gear had to some extent become an end in itself and one had to spend a lot of money just to set it up every day before you photographed a single frame of the actual subject matter.
3. Light. These newer cameras have big sensors (the Canon 5DII in particular has a very large sensor for the available price) which means they can get a good-looking image with way less light than a typical pro video camera (and in turn that makes it easier to control the focus of the image). So you don't need truckloads full of lights...or the time to set the up...or all the noise of a generator to power them...or a bunch of grips to lift and carry them...and you don't have a forest of aluminum stands with lights and reflectors all over the set: which means you have a great deal more freedom in where you put the camera and how you move it around.
In short, they are awesome. There are some limitations, and some things you have to do differently in order to maintain image quality compared to other methods...but they are not that onerous and the cost savings are enormously worth it. I would never want to go back to the style of a big industrial set festooned with heavy equipment and crews. Small is beautiful.