The Truth On The Veil 

The “veil” in the Quran was a traditional desert headdress of Hebrew people. The Arab nation which is a mix of Hebrews also took this on as a protection against the sun.
The Quran commands women to “cover their jewels” not hair-BUT the hair was already covered as a desert protection.
The Muslim veil was to be wrapped around the neck to hide the breasts from unwanted attention from men. 
It was a very different time back then. It was helpful advice and not at all commanded. 
Piousness can today be demonstrated in many ways to keep the integrity of a woman. 
If you aren’t in the desert there is no need to wear it. You can dress modestly.
Different sects and even individuals will see the veil differently. Depending how material you are from more spiritual perhaps.