So there is no particular reason to use blinn instead or phong, only the tweak can make the difference or there are particular cases where Ward (for example) is more efficient than the other ?
If by efficiency you mean calculation speed, Phong is fastest, followed by Blinn, and then Ward, but these calculations are usually just a minor part of the rendering compared to everything else. All in all, it comes down to what looks best.
I would actually use Ward for fabric, and for wood that is not overly shiny. I find ward is pretty glossy looking even at .98-.99 glossiness, so the “minimum” is pretty glossy by comparison. THis makes it pretty handy for fabrics - you don’t need to go as low and thus push render times up higher. Seems to work for me anyway.
Otherwise I’m with Vlado: blinn is the one I usually use for shinier plastics and non-metals, but the difference between that and phong is usually pretty minor in practice. YMMV