One needs to be careful on taking words out of context, or even assuming a word should have a literal meaning; remember the poem was ment to be read out loud and the sound of the words had meaning too.
In this case I think that by 'unreflecting' Keats means -
thoughtless - without considering the consequences - passion over sense.
Poemhunter has had some strange choices as poem of the day but this takes some kind of biscuit.
Wilmot is regarded by some as the formost poet of his day, but to call it well written is bending some definitions - although the comment 'many write but few like this' is true.
But usually as children on toilet walls.
In fairness it should be pointed out that the poem was not ment to be published on a site for millions of families to read, but to be passed round, hand written, at court.
The subject may have been sitire. Who knows!
The man was personally well thought of in his day, and well liked.
Other of Wilmots 'verse' is much cruder, and distasteful.
Other, clever and almost funny.