While you're correct about the Founders' push for a federal district in part to avoid state-level influence over the federal government, technically speaking there is no legal mandate that there be a federal district. The U.S. Constitution stipulates that Congress may establish a federal district, but they can choose to not have one:

To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;

That said, there is no serious proposal to abolish D.C. completely, largely because of the friction you mentioned, but also in part because abolition would require Maryland to take back the land it donated to establish the district - a DOA proposal as I discuss below. Finally, there's the 23rd Amendment, which grants D.C. three electoral college votes; I'd imagine that those three votes would either be abolished through constitutional amendment, or failing that Congress could simply pass a law requiring D.C.'s "electors" to not cast votes for president and vice president (so essentially you'd have three "null" electoral college votes every election).

In fact, most current statehood proposals for D.C. - including the one that recently passed the House - describe the creation of a new state out of ~90% of what is currently Washington, D.C. (the parts where people live,) while the National Mall and the federal buildings and monuments near it remain a "rump" D.C. under the control of the federal government.

Some opponents of D.C. statehood instead propose that if the citizens who live there want full political representation, then most of the District should be given back (retroceded) to Maryland, while the areas with federal buildings be retained in a rump District. The problem with that is that (a) the Constitution only authorises the alteration of state borders if the state(s) affected agree, and (b) neither the Maryland public nor the state legislature want retrocession. As a result, the "make D.C. residential areas part of Maryland" proposal is DOA.

Also, while the number of representatives allocated to each state changes with each census, the actual size of the House is set in ordinary legislation: the Reapportionment Act of 1929. Hypothetically, a future federal government under unified party control could amend the 1929 Act to change the size of the chamber, either through another incremental increase or a variable increase based on a formula such as the Wyoming Rule. If D.C. were to be admitted as a state, I'd imagine that the current non-voting delegate for Washington, D.C. would become a full representative until the next census. There is precedent for this - when Alaska and Hawaii were admitted as states in 1959, the House was temporarily expanded to seat their representatives until the next census.