I suppose that depends on what you're growing. I would never consider growing azaleas or evergreens hydroponically though I may root cuttings that way.
If you're going to grow food, on the other hand, I do it for a number of reasons:
pest control - a lot of insects place there larvae in the soil and it later crawls onto plants. no dirt pests removed.
pathogen control - many soil borne diseases are eliminated by not using soil.
weed control - no dirt, no weeds
comfort - it's much easier to tend to your plants (and look for those pesky leaf larvae) from a standing position. soil gardening is prohibitive of beds raised to waist level.
water control - with hydro I can set up a continual water system or one on a timer and don't have to worry about neglecting watering my plants for a week or so. not that you can't do that with soil, but you'll still need to adjust things based on environmental conditions.
and finally, less environmental impact - not so much for me (I'm small potatoes), but on a larger scale, you could recycle your nutrients and thus not dump anything back into the soil. with soil gardening, you fertilze a plot of dirt and hope you plant gets enough, your weeds don't get enough, and not too much leeches into the subsurface water. again for me not relevant. I typically water plants in my yard with the spent nutes. But, if and when I go production, I plan on 100% recycling nutrient.

Thanks for the response. I would think then that if I only want to propagate normal plant found around the yard and garden then the hydroponics method would not be of much benefit? Everything that I start from seed or cuttings would wind up in the ground sooner or later. I guess I just wondered if starting some of the smaller cuttings in this method would be worth the effort.

if all your plants are eventually destined for soil then dont use hydroponics.

I don't know a good cloning box roots cuttings pretty quickly, but it would probably be on a plant by plants basis.
you just can't let the roots get too big before transplanting or you'll have difficulty getting them in the soil.