old man,
If a black hat and dark jacket are respectful, and possibly the only respectful clothing for men, is it also necessary to any extent that these garments be clean?
Absolutely. I don’t think anyone here is arguing that there is no requirement to dress nicely for davening, which would obviously mean dressing cleanly. The argument is a halachic/cultural one over what specific clothing fulfills the requirement.
Some seem to interpret the halacha to dress nicely as meaning whatever the surrounding culture deems formal and nice. Therefore, since hats are largely out of style in the U.S., and a jacket and tie are considered formal (and in some places, it’s ok to even go without the jacket, or the tie!), they believe a hat is not required for davening.
Others seem to interpret the halacha to dress nicely as meaning whatever the surrounding Jewish community deems formal and nice. Therefore, since some communities consider hats and jackets to be formal attire, they believe a hat and jacket are required for davening in that community.