George W Bush put bronze statues of his Scottish terriers Barney and Miss Beazley in his presidential library. Richard Nixon had a chunk of the Berlin Wall installed in his. In Franklin D Roosevelt, his own face appears on an 8ft stone Sphinx. And Bill Clinton graciously agreed to display that cigar.

OK, that last one is made up. Because, while they can include odd memorabilia, presidential libraries are all-American vanity projects, burying the worthy archival stuff – letters, speeches and film reel – in great monuments to political hubris.

Chicago is abuzz with debate about Barack Obama’s physical legacy as plans take shape for his own library. Since Herbert Hoover (1929-33), the construction of these museums has become customary in leaders’ home states.

Memorable memorabilia (clockwise from right): horses jump pver the Berlin Wall at George Bush’s centre; FDR’s sphinx; a dummy of Herbert Hoover fishing; the statue of George W Bush’s scottie dogs, Barney and Miss Beazley Composite: Getty Images/composite

Most presidents also choose to archive themselves under their own buildings. But how do you distil a life and a presidency under one roof? In Chicago, where Obama began his audacious political journey, there is concern about plans to include in his library a digital archive rather than stacks of papers and books. More than that, the suitably modern, $1.5bn edifice in the city’s Jackson Park will include a basketball court, a yoga space and a test kitchen.

In a scathing column in the Chicago Tribune, Ron Grossman called out the plans as unworthy of the tradition. “Mr President, I’ve got to tell you: the renderings for your museum are … more likely to congeal than stir blood,” he wrote, adding: “Is [this] how you want to be remembered? As the healthy-eating and meditation-advocating president … That’s not how I want the story to come down to my grandchildren’s children.”

The focus on activities reflect Barack and Michelle Obama’s fight during their eight years in office for healthier living and exercise – and their desire for a library to be a living, fun-filled space rather than a dusty mausoleum where speeches are played on a loop.

Where it all began: the Herbert Hoover Presidential Library, in West Branch, Iowa. Photograph: UIG via Getty Images

The plans may change before the project is completed in 2021. In the meantime, there can be no harm in wondering what the 15th presidential library – that celebrating Donald Trump – will look like. Might a holographic Kellyanne Conway welcome visitors to the food court in the lobby? Gold lifts to the replica Oval Office on the 121st floor? Wigs in the gift shop?

Whatever it contains, we can safely predict that the Trump library will be the greatest presidential library in US history. A lot of people will be saying that. But be warned, Donald. According to another tradition, library visitor numbers tend to reflect the approval rating of each president at departure. That bodes well for Obama, who left office on 59%. But Trump’s rating has dropped from a high of 45% to a historic low of 37%, which may yet test even his powers of crowd-size exaggeration.