Even if I were a closet atheist (which I’m not), I’d support public prayers just to p*ss off the ACLU and their cohorts who wish to make atheist the de facto state religion.
Atheists deserve respect just like believers. That means I don’t use the law to restrict their speech anymore than they use the law to restrict mine. That’s what happens in a free country. We all get to practice our religion or non-religion so long as we don’t force others to participate.
I also believe that’s the intent of the constitution. The founders would have laughed at anyone who said a government official couldn’t invoke the name of the Lord while acting in an official capacity, and they didn’t have to invoke the name of every possible deity in order to be fair either.
BTW, a non-religious event could be considered coercive in an area where most people believe a particular religion. That’s what some people don’t seem to understand. They think it’s coercive to mention Jesus for example, but it’s also coercive to drive the name Jesus from the public square!
If you were an atheist, you wouldn’t consider atheism a religion, just like not playing basketball isn’t considered a sport.