You’d still end up with an indigenous population - many of the busboys, maids and other minimum (and sub-minimum) wage workers would rather live near their work, even illegally, than commute who knows how far (and at what cost) from elsewhere. And along with them you’ll get all of the services such a population requires. You’ll end up with a city consisting of a few government employees and thousands of low- or no-income residents. A lot like DC, actually.
You’re assuming the normal doughnut structure of a city in the U.S., with the poor living in urban blight near the city core, and the rich living out in the suburbs. In fact, it doesn’t even happen completely like that in DC: there are desirable neighbourhoods, like Capitol Hill and Georgetown, where comparatively well-off people live – who are often working for the government, but may be working for lobbyists, or even in more “normal” occupations.
However, if DC were a county, it would be the second most Democrat-leaning county in the US. (The most Democrat-leaning is Bronx County in New York State). And it’s not just the poor black people in SE Washington voting Democrat – a lot of the richer white folk in NW Washington vote Democrat too. This would be a strong political reason why DC can’t get voting rights in the Congress: for the foreseeable future, its representative would be Democrat, and no Republican state would ever vote for that.
But, for an example of a capital district which is not “busboys, maids and other minimum (and sub-minimum) wage workers”, look at the Australian Capital Territory. There, the residential areas close to the Parliament House and the main government office buildings are highly desirable, and the Australian equivalents of “busboys and maids” couldn’t afford to live there – they tend to live further out. That’s the usual Australian pattern: inner city suburbs are more desirable (everything else being equal), and poorer peoiple live in the cheaper outer suburbs.
In India, the National Capital Territory of Delhi has its own legislative assembly, directly elects 7 members of the lower house of parliament, and indirectly elects 3 members of the upper house of parliament.
There is a movement to make Delhi a full-fledged state.
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(Bolding mine): But, that itself is part of what the drafters were trying to avoid by creating DC. While Congress sat in Philadelphia under the Articles of Confederation, they found out that Pennsylvania could not be relied upon fully to back up the Congress, even in the face of an armed riot. So not only did they create a Federal Government with more and sharper “teeth” than the Confederation’s, they granted it a whole county-sized space to set up its own day-to-day operational support, over which it would be in command.
In any case, they may have expected that even so the Capital District would remain a relatively small “company town”, with a large transient population of whoever worked for the sitting officials for the duration of their terms plus the military garrison; they probably did not foresee the Federal Government becoming the large bureaucracy it became in the 20th Century nor its capital’s permanent resident population becoming comparable to or greater than some states’.
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With other federal districts and their adaptations to enfranchise their residents, you have an element in the respective constitutional histories to consider and which I touched upon in an earlier comment – they contemplate a concept of what someone I once spoke with called an “asymmetric federation”. You allow some subnational entities, considered creatures of the legislature, a voting representation under terms different from the “sovereign” constituent federative entities.
Under the US Constitution, however, the constituent components of the Union are only “the several States” and the standing and conditions under which they participate in the Union are to be equal: 2 Senators, one or more Representatives according to fraction of population, Electors equal to the sum of those two groups, uniform taxation, etc. Nobody else gets anything unless the Constitution itself mentions it, so to grant Electoral Votes to DC took a constitutional amendment. There is no provision for a category of Senior Territory/Junior State with an abridged but voting Congressional representation, the Territories are Congress’ real estate to do with as it sees fit, as far as this Constitution is concerned (All the various forms of classifying and running the nonstate components – organized/unorganized/incorporated/unincorporated territory, commonwealth, “zone”, etc. – are set forth in a score ad-hoc statutes, treaties or court decisions, not even in one single ordinary Federal law).
Another thing is that, as far as I’m aware, the District of Columbia was the first federal district established under a democratic constitution, so when the US founding fathers set forth its rights under the Constitution they may not have fully considered that they were depriving its future residents of representation. However, when later federal districts were established, they had the example of DC, so they could avoid its voting rights problems.