Daniel Pipes argues
that they "present a security risk," and that they "facilitate non-political criminal behavior." He even cites a health issue:
British research offers another reason to drop the burqa and niqab, finding that covered women and their breast-fed children lack sufficient amounts of vitamin D (which the skin absorbs from sunlight) and are at serious risk of rickets.
Is there a parallel in American culture that gives us a clue as to whether this is a good idea? Nuns' habits dont' count, because they don't cover the face. Klan hoods cover the face, though. Church of the American Knights of the Ku Klux Klan v. Kerik upheld a New York State statute that prohibits certain public mask-wearing:
S 240.35 Loitering.
A person is guilty of loitering when he:
4. Being masked or in any manner disguised by unusual or unnatural attire or facial alteration, loiters, remains or congregates in a public place with other persons so masked or disguised, or knowingly permits or aids persons so masked or disguised to congregate in a public place; except that such conduct is not unlawful when it occurs in connection with a masquerade party or like entertainment if, when such entertainment is held in a city which has promulgated regulations in connection with such affairs, permission is first obtained from the police or other appropriate authorities;
Burqas and niqabs appear to violate the law, since they are not worn for entertainment purposes.
In a 2004 FindLaw article, Rutgers lawprof Sherry F. Colb stated her objections:
In particular, the opinion was wrong to reject the Klan's First Amendment claim that masks constitute symbolic speech. And it was also wrong to reject the notion that an organization's members have a right to anonymity that might include appearing in public wearing masks.
I am an originalist, thus I reject the first claim. "Speech" is what every human in the late 1700s defined as speech: verbalized expression. If the Free Speech Clause were so broad as to cover even nonspoken expression, then the clauses protecting freedoms of the press, religious exercise, and redress of grievances against the government would all be redundant. In fact, just about every human activity can be interpreted as expression.
As for the latter claim, there is no Constitutional right to public disguise. That is an issue for legislators, not judges.
I suspect that the NY law also had in mind ski masks. Pipes' chief argument is the disguise-for-criminals concern; he cites specific examples of Islamic dress being used in such manner, and could bolster his case by noting that the burqa and niqab do not draw as much suspicion as the ski mask, making them a superior disguise. However, I suspect that if face-enclosing Islamic wear were criminalized, crooks would find other ways to disguise themselves without drawing attention. A mere hat and sunglasses hide a lot.