I believe the Prophet صلى الله عليه وسلم covered his head most of his life with a turban. Now is it better to copy that exact headgear or rather the lesson from this is it's better simply to cover the head with whatever headgear (cap, topi, winter hat, turban, etc). There was a point made in a YouTube lecture that the Imams of the haramain don't wear a turban and it would better to do that - closer to the Sunnah.
I am sure this has been answered several times on this website, still I would like to add a few common sense thing to it.
If you have experienced travelling to extremely hot weather (50°+ room temperature), you would find that people generally cover their heads to protect themselves from heat. Thanks to modern construction and facilities people are doing this less often.
The weather of Arabic desert is extremely wild, it is unbearable to move in it without not just covering the head but the complete face, to protect from heat and dust. It is still the culture of Arabian Peninsula. Probably that was the reason that it was sunnah to cover head while praying, but there is no hadith that prophet call it a sin to uncover the head. However immams and Muslims should still follow the sunnah.
There are some exceptions too... Muslims on pilgrimage observing Ihram should not cover the head or face no matter how hot or cold it may be. Because Ihram (no matter whichever color or class they belong to) represents the equality of all humans.