Is this what the niqab is supposed to signify?

Bret Stephens has an interesting take on the purpose of the niqab - or face veil - in today's Wall Street Journal. Here are some key excerpts:

Seen from a narrow angle, it's easy to tie oneself in knots debating the correct attitude of Western societies toward the veil. The liberal says: People generally ought to be entitled to dress as they choose. The liberal also says: Veiling the female face isn't merely an expression of sexual modesty but an obliteration of a woman's public identity and hence a violation (even if self-imposed) of her political rights. The conservative says: If religious freedom is a bedrock Western value, then the rights accorded to the Amish or Hasidic Jews to dress as they do must also extend to ultraconservative Muslims. The conservative also says: Liberal societies cannot allow illiberal and separatist practices to flourish under the banner of multiculturalism, particularly if those practices are often enforced by violence.

Yet all this misses the fundamentally tactical element of niqab. "It's about enforcing separation," notes a former senior French Interior Ministry official who helped draft his country's 2004 ban on religious headgear in public schools and government buildings. "It is best understood as an intra-Muslim show of strength, a way to intimidate their own women, a way to intimidate the infidels, a way to make themselves more visible, a way to make sure no one strays from their world vision."

Is this how the Prophet Muhammad intended the niqab to be seen?

Did he really perceive it to be the symbol of Muslim arrogance, oppression, and Islamic terrorism that it has become?