Bismillahirrahmaanirrahiim. I hope I’m able to get the point across.
If a world renowned doctor advised you to apply the SPF50 sunscreen because it will protect you from the harmful rays and thus will lower the chance of getting skin cancer, you would most likely follow right? No? Ok maybe depending on how much you believe that doctor.
Muslimah (female muslims) wear the head covering because it is a commandment of Allah (subhaanahu wa ta’aalaa). All the rest of the benefits are like secondary. For example to practice modesty and protect ourselves etc.
We believe and we obey. It is because we have come to the conclusion by our intellect that Allah is our God and Muhammad (sollaahhu ‘alaihi wasallam) is His messenger, then everything falls into place.
I shall give you another example to demonstrate what I am trying to say. The companions of Prophet Muhammad (sollaahhu ‘alaihi wasallam) just obeyed when pork is forbidden for consumption. They just obeyed. Poof. Imagine now when muslims are asked why we are not allowed to eat it, we will most likely have answers along the lines of ‘Scientists have proved that it is not healthy’.
The companions just obeyed because they know that everything that come from Allah and His Messenger are good for them. They do not do it because of the ‘healthiness’ (since they don’t have the means to know at that time) but rather because they believe.
We just obey because we believe.