I still disagree that your verse also includes brother so and so being asked to stand up and pray in his local church for the sick and for the salvation of souls before the offering plate is passed. I know about Matthew 6:5. Brother So and So probably isn’t even expecting any sort of reward and wasn’t even expecting to be asked to pray.(That is how many a Baptist preacher likes to keep things “lively”)
I think Luke 18:9-14 explains the sort of thing God is looking for and what he doesn’t in praying people...and remember...both went to pray in the temple.
Sure the most fervent deep felt prayers are to be done privately and public over done prayers will get nothing back but faint praise.
Praying out loud, leading a public prayer isn’t wrong - the point is when one prays out loud in a sanctimonious fashion or about their self-afflictions “Oh God, please help me not eat this much this week.” or “Oh God, please let me continue to fight against Trump and the evil he spreads against America” - These aren’t “prayers”