If Civic Duty is your concern, why not take the "Under God" out and restore the Pledge to the pre-1954 non-Knights of Columbus version? That one was all about Allegiance to the country and nothing to do with religion at all.
The answer is that because they recognized in the 50s (perhpas relearned or rediscovered is a better term) that this nation was founded on those principles and has everything to do with, from its founding, the idea that there is a God in Heaven, regardless of persuasion, that watches over the affairs of man, and who endows upon mankind their unalienable rights.
Without that knowledge, it is impossible to understand the basic founding principles of this Republic and the resulting civic responsibility. John Adams said it best:
"We have no government armed with power capable of contending with human passions unbridled by morality and religion. Avarice, ambition, revenge, or gallantry, would break the strongest cords of our Constitution as a whale goes through a net. Our Constitution was made only for a moral and religious people. It is wholly inadequate for the government of any other."- John Adams, Oct. 11, 179
That Adams quote was 1798.