The reason why we wear a hat is quite complex. For some, it is a social thing, for others it is a hard standing minhag (Hello Yekkis), and for some they use a diyuk from a be’er halacha by benching (it says there one should wear bigday tefila) to compare it to shmoneh esrey, so that’s why some wear a hat. I had a long ( 3 hour) discussion with my rav who said all of these reasons yet we went into much more detail than i just said obviously.
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