My understanding of godfearing is that, one fears the consequences of ones actions, and God is in control of everything, so "one fears God".
Also the ultimate consequence of heaven and hell, which seems to be linked to fear, in the Quran.
In that way, a translation of godfearing makes sense.
"The godfearing are the best of people" says the Quran.
However it also states that "The righteous shall have no fear".
If you are righteous and have no fear, the word godfearing might mean little to you, and godconscious would seem a better alternative.
Indeed even loving God, or worshipping god, which is what love of God is, would seem better.
Maybe some aspect of taqwa has got lost in translation?
However, it certainly NOT is an unnatural attitude to be emulated. It comes naturally. Probably from fear of heaven or hell.