The original reason for using duotones was simple economics:
"Duotones are often used in the printing world where a photograph is included in a publication and where the publisher wants to use some color on the page but not pay for full color printing." (
http://digital-photography-school.com/convert-duotones-photoshop/ )
However, duotones have become one of the standard tools for graphic designers who want a dramatic, edgy graphic look. Just go to Google Images and search on {duotone design} and you'll see many examples where this technique has been used for effective communication, quite independently of the original cost benefit.
Photography is a different story compared to graphic design. You will see lots of examples of people who initially play with the duotone technique to give an absolutely nutso, exaggerated look to their conventional continuous tone B&W photos. Some people think this is art. Maybe, coupled with other factors, it is, but this is probably what you reacted negatively to. However, IMHO, most serious B&W photographers move on from this point, and use duo, tri and quadtones to impart more subtle effects to their B&W images, with quadtones being able to impart the most subtlety. Here are two examples of this:
http://static.photo.net/attachments/bboard/003/003mCg-9542484.jpg
https://lh3.googleusercontent.com/-...,0000210fffcefa0f/lauren-quadtone_JJE3396.jpg
And, here's a very nice tutorial on quadtones that show the variety of effects one can get, discuss some of the pros and cons, etc.:
https://www.youtube.com/watch?v=AerxJgOvb1E&feature=colike
Note that there are many different ways to create quadtones and similar effects besides the native tools provided in PS. The above tutorial was from Topaz. Tiffen DFX has a very nice mode where you can set different tint colors, contrast, etc. in each of ten(!) tonal ranges, harkening back to Ansel Adam's historic "zone system".
Among high-end B&W photographers probably the best known use for quadtones is in printing. Low end, conventional inkjet printers have only four inks, CMYK. Go up a bit in price and you will see printers that use a few more colors, eg, two shades of black, maybe a couple of different magentas, etc. Among high-end B&W print afficionados and simply people with good eyes, none of these inkjets does as good a job on B&W prints as an old-fashioned B&W print made in the darkroom.
To satisfy the desire to do better, companies started putting out kits (ie, inks and software) that generally goes under the name, Quadtone Raster Image Processing (RIP) system. With these, instead of having only one or two black inks, they supply 4 or more gray and black inks and can achieve absolutely beautiful prints that compete will with prints make in the darkroom. There has been a huge amount of material written about this, and while it's somewhat of a nich, high-end market, Quadtone RIPs are probably not going to go away.
Here are links to two companies that sell Quad Tone RIP (raster image processor) systems:
http://www.quadtonerip.com/html/QTRoverview.html
http://www.americaninkjetsystems2.com/learningcenter/anytone_beyond_quadtone.html
HTH,
Tom M