We map city boundaries at all because a place node doesn’t communicate an inherent area, and a fuzzy point cloud of addresses doesn’t really equal the city limits. Some Washington, D.C., addresses are physically in Maryland or Virginia and vice versa, because postal cities and ZIP codes are based on delivery routes, not boundaries.
That said, no, the Washington boundary probably does not need to be an administrative boundary to satisfy the common geocoding use case I described. Ignoring the history, I would liken it to the boundary for Alaska’s Unorganized Borough or Maine’s Unorganized Territory: a process of elimination, except that in D.C. there’s nothing to eliminate in the first place. The Unorganized Borough is currently mapped as an admin_level=7 administrative boundary, as opposed to the boundary=census boundaries for census areas. The UT goes unmapped, but at a more local level, Maine’s gores are admin_level=8, on par with its governmentless townships.
Washington definitely exists in the present day, not just as a historic artifact, and it has a well-defined territory. But as you point out, it’s administratively irrelevant these days, just a geographic catch-all. Could we tag its boundary as boundary=place, similar to the well-defined but governmentless neighborhoods in some cities? People looking for the boundaries of all the cities would still find it via border_type=city, but not via admin_level=8.