To prefix a statement about oneself with 'as' in the way you describe is to claim the expertise or status of what follows:
As a gardener, I'm telling you that roses won't grow well in chalky soil.
As a resident of Manchester, let me tell you it rains a lot there.
As a non-smoker, I find the smell of cigarettes unpleasant.
Such sentences may suggest a level of pomposity, but in general they are not automatically funny or amusing.
July 13th 2018: Donald Trump is visiting Britain, and protesters have launched a 20 ft tall "Trump Baby" blimp in London. The Guardian reports a visitor saying to one of the organisers: “As an American it means so much to us that you have done this. Thank you so much.”
Guardian blimp story and pictures