It is very popular. Most brands have adopted it. The only hold outs are Nikon and Canon. Pentax, Sony and Olympus use in-body stabilization on their latest lineup of DSLRs and mirrorless cameras. Panasonic has 2 high-end models with stabilization and the rest without.

There is a tremendous advantage in having stabilization in the body. Not only do you incur the cost only once as you said but it also works with every lens, many of which do not have any stabilization counter-part: Think fisheye, tilt-shift, ultra-bight lenses, etc. Even third-party legacy lenses can easily benefit from stabilization, although you have to manually enter the focal-length into the camera.

Another neat aspect over a photographer's lifetime is that each time you buy a new camera it comes with a new - and usually improved - image stabilization mechanism. Most photographers change their cameras much more often then lenses. Some lenses I use are over 20 years old while my cameras get replaced at most every 2 years.

For mirrorless cameras, Olympus, Sony, Pentax, Panasonic (some models) all have it built-in. Nikon 1, Canon M and Fuji X and have no camera with stabilization and some Nikon 1 models have no moving parts at all (no shutter, no mirror) which brings other advantages.

For DSLRs, the difference is that optical stabilization is visible in the viewfinder while sensor-shift is not. For telephoto lenses, this makes it easier to aim but that does not mean stabilization is any less effective. The theory though is that lens based stabilization can be optimized for the particular lens it is in.

With the Panasonic GX8, the argument is moot. That camera uses both simultaneously, using each to correct for different types of shake. Planar shift gets corrected by the sensor and rotational movement gets corrected by the lens.