If amateur architect James Diamond had his way, the U.S. Capitol would’ve been a modest, two-story building topped by, not a statue of freedom , but a honking-huge weathercock. Had John Russell Pope realized his vision, the Lincoln Memorial would’ve loomed like a pyramid lifted from the sands of Egypt. And had D.C. greenlit a proposal from Jim Allegro and Doug Michels, the White House would’ve stood opposite a 300-foot-long public couch (complete with a flatscreen TV).

Alas, none of these plans ever materialized–to the District’s benefit, no doubt. But that hasn’t stopped the National Building Museum from pulling old models, blueprints, and drawings out of the trash can and mounting them on display in Unbuilt Washington, a captivating new exhibition about the Capitol city that might’ve been.

Proposals like that make you realize: Things could’ve been a lot worse.

Every city has an anthology of architectural “what ifs.” There’s Manhattan with its Robert Moses highway. There’s Chicago with its mile-high skyscraper designed by Frank Lloyd Wright. But not every city’s architecture endeavors to project the political ideology of a nation, as D.C.’s does. So when you see that a palatial mansion, which would’ve seemed fussy by Louis Quatorze’s standards, was tossed in favor of the neoclassical White House we have today, you can take that as an endorsement of democratic ideals over the silly hierarchies of old Europe. And you can look at the crisply proportioned U.S. Capitol as a high five for reason over absurdity (seriously, Diamond’s weathercock was ridiculous; curator G. Martin Moeller Jr. likens it to a “giant chicken in distress”). Even if you despise the arch-formality of the Mall, which I do, proposals like that make you realize: Things could’ve been a lot worse.

But they also could’ve been a lot better. Imagine if the Smithsonian art gallery had been a stylish asymmetrical building by Eliel and Eero Saarinen, to name one unrealized project. Or if Leon Krier had brought off his half-baffling, half-brilliant idea to flood the Mall, Venice-style, then fill nearby blocks with mixed-use buildings, effectively creating bustling neighborhoods where fortress-like federal enclaves stand today.

Perhaps the most innovative idea was a 1966 plan by Chloethiel Woodard Smith & Associate Architects for a walking bridge between East Potomac Park and the Southwest Waterfront. A former shantytown, Southwest Waterfront was demolished in the middle of the 20th century then redeveloped (rather unsuccessfully) and has long exemplified a vexing paradox of D.C.: The city is terribly segregated–part pristine museum, part slum.

Ingeniously, the bridge would’ve been packed with stores and other businesses, like a sort of latter-day Ponte Vecchio. “Although the project was relatively limited in scope–a single bridge spanning between the Southwest waterfront and East Potomac Park–I think it would have had a significant impact on the urban renewal area of Southwest D.C. and might have become a regional draw,” Moeller tells Co.Design. “Lined with shops and restaurants, and free of private cars, the bridge might have provided a vibrant commercial center for Southwest, which the shopping mall that was built [there] never succeeded in doing.” Such proposals could’ve helped make the District a lively urban mecca, instead of the strange, schizophrenic city it is. Put another way: The capitol of the democratic world could’ve looked a lot more democratic.

[Images courtesy of the National Building Museum]