One suggestion does not make a doctrine. Corinth was a city of sailors and prostitutes. It was important in that society to disguise between women woman who were prostitutes and women who were not. At that place and time, nothing to do with our habits and practices today. I wear a hat in winter when it is cold. That is very accepted in Canada. But there is no tradition in western society that a woman needs to wear a hat to distinguish herself from a woman of ill repute.
It is legalism to try and earn your righteousness by what you wear on you head, or anything else. We are saved by grace through faith.
If every epistle in the NT recommended wearing a hat for women, it would still be legalism to wear a hat to sanctify yourself. Instead, we are sanctified by the power of the Holy Spirit in our hearts. God justifies, sanctifies and glorified.
"And we know that all things work together for good for those who love God, who are called according to his purpose, 29 because those whom he foreknew he also predestined to be conformed to the image of his Son, that his Son would be the firstborn among many brothers and sisters. 30 And those he predestined, he also called; and those he called, he also justified; and those he justified, he also glorified." Romans 8:28-30
Read Hebrews! "For by one offering he has perfected for all time those who are made holy. 15 And the Holy Spirit also witnesses to us, for after saying,16 “This is the covenant that I will establish with them after those days, says the Lord. I will put my laws on their hearts and I will inscribe them on their minds,” 17 then he says,“Their sins and their lawless deeds I will remember no longer.” 18 Now where there is forgiveness of these, there is no longer any offering for sin." Hebrews 10:14-18.
The law is written on your heart! And no need to wear a hat or do anything else to earn forgiveness. We repent if our sins when we believe, and God cleanses us of all unrighteousness. 1 John 1:9