Yes, I have calculated and paid tax on all gifts that I have ever given in excess of the reporting threshold (i.e. none, because I don't give away gifts worth tens of thousands of dollars).
To the extent that we have received large gifts from relatives, yes, we've reported those accurately to the tax authorities in two different countries. There was no tax due, but I would not have objected philosophically to the gifts being taxed.
Huh, sorry, as a Briton it's quite literally a foreign concept to me; I thought I was joking.
In the UK there's inheritance tax to pay over a threshold if you die within 7 years of making the gift, but otherwise there's not a 'gift tax'.
The situation you describe still isn't the same as declaring it as income though - assuming you are working, if it were taxed at your marginal rate of income tax you'd already be over any threshold no matter how small the gift.