The method you describe is a carry-over from heating crawl-spaces in the extremely-cold areas. The idea is not so much to heat the floor above entirely, but to temper the area so it is not near outdoor temperatures.
Install a damper in the duct that supplies the air. Then you will be able to see the result of closing it off in the winter - without totally abandoning the idea if it proves necessary. With foam on the underside of the floor the air to the space will be less necessary for a comfortable floor; but without the air the ducts would get such cold air in them that the blast of cold air from the ducts when the blower starts again (if it is not constant flow) would sure make a bare-legged cook jump.
Underfloor radiant heat would get rid of the heating problem with much less wasted energy; but you have what you have. I imagine you are enjoying the hydro-electric rates there, so electric radiant heat would be easy to install and as much to run as any fuel.
www.heatpro.info heat/cool right-sizing
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