In 1820, the U.S. Supreme Court issued Loughborough v Blake, 18 U.S. 317. It seems to suggest that the Court believed Congress is free to provide for a voting member for the District of Columbia in the U.S. House of Representatives.
The case concerned whether Congress could tax residents of the District of Columbia. But it also says this: “Although in theory it might be more congenial to the spirit of our institutions to admit a representative from the District, it may be doubted whether, in fact, its interests would be rendered thereby the more secure.” Thanks to Michael Warnken for this. Here is a link to the opinion.