As already said, a motorcycle helmet is already banned in a lot of public places a virtually a requirement to be taken off inside all buildings. I want to see a similar restriction on the full face vile as it's harms society. Harms society in what way i hear you ask. Segregation... it stops women effectively communicating with anyone outside of their community.
I have spoken to loads girls in hijabs, most of them are surprisingly very affable and sweet. But i am yet to bump into and speak to anyone in a full face vile because they tend to avoid contact, run around with their kids in tow and tend to barge past you as if they have some god given right of way.
If someone doesn't want to interact with society, or with you* then what's the problem? As others have said there is a difference between real security concerns (such as in banks and at airports), where there are generally already rule regarding full face veils and walking around on the street.
Yes, there is an element of oppression with some that wear full face veils, but just banning them outright is not the way to go. For many it would be akin to banning t-shirts and tops on women, forcing them to walk around topless. We don't see it as the same, but people from certain parts of the world, having grown up with certain cultural norms would.**
You're probably never going to persuade first generation immigrants from certain areas of the world, especially if they are older, to stop wearing a veil, but the likelihood is their children growing up in the west won't wear one so it's a self solving problem using our education systems and cultures.
*thats not a slight at you, thats a general "you"
**actually, ironically it could well be construed as a similar battle to the free the nipple campaign, where women are fighting for equality with men for their upper halves - I.e. In many countries (and by that I mean western countries like the US and UK) women aren't allowed to walk around topless, even if they want to. Why can't we just let people wear (or not wear) what they want?