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Dye sublimation is really geared toward small prints. In the long run, it's not as cost-effective as inkjet, because as you noted, the consumables are expensive. A particular quirk of the technology is that the cost per page is independent of the density of the print--in other words, if all you print are low-key images, the cost per page is the same as if you print high-key images; whereas for an inkjet, the cost per page is mainly a function of the amount of ink laid down per page.
Very high-quality inkjets use 6 or more colors, and sometimes as many as 10 or 12 (though not necessarily all in the same print). The output is extremely fine, and the individual drops are only visible under high magnification. But a dye-sub print is literally continuous tone--there is no dithering applied.
Proper media and storage will give either technology archival quality, so that is not a concern. Both types of printers need some kind of calibration.
Inkjet technology has advanced to the point where proper maintenance prevents nozzle clogging, but the ink is still expensive. Personally, I've not found any truly satisfactory printing method. If you print photographic color in high volumes, inkjet is pretty much the only game in town. If you print general color graphics, color laser is your most economical and hassle-free solution. If you print the occasional photo, then you're better off having it sent to a service. The cheap inkjets are not worth buying, IMO. Then there are the more exotic technologies like dye-sub and solid ink. I think these are mostly relegated to specialized applications; e.g., ID badge printing, small prints, and business applications.
Photographers are so used to paying through the nose for their gear that we pretty much bend over when it comes to photo-quality digital color print solutions. Several thousand dollars for a large-format inkjet is just another expense to be added to the thousands spent on lenses, bodies, and studio lighting, but the technology and the ink is inherently very, very cheap to produce.