When the CDC mailed a coronavirus advisory to many U.S. households in March 2020, the front of the large postcard read, “President Trump’s Coronavirus Guidelines For America” in all-capital letters. It wasn’t long before some questioned whether the mailing was intended, at least in part, to help promote Donald Trump in an election year.

Soon after, as the pandemic pushed the United States into a recession, the federal government prepared to send direct-aid checks to millions of American households. The Wall Street Journal reported at the time that the president told his team that he had a specific priority: Trump wanted his name on the checks.

The article quoted a former senior Treasury Department official saying that, under normal circumstances, “a civil servant — the disbursing officer for the payment center — would sign federal checks.” In the spring of 2020, the Republican incumbent didn’t care about “normal circumstances”; he cared about self-indulgent, election-year self-promotion.

Trump got his wish: The president wasn’t legally authorized to sign disbursements from the U.S. Treasury, but his administration ensured that the congressionally approved checks featured the words “President Donald J. Trump” were printed on the fronts of the checks.

More than four years later, his successor wishes he’d done the same thing. President Joe Biden told a Brookings Institution audience:

Within the first two months in office, I signed the American Rescue Plan — the most significant economic recovery package in our history. I also learned something from Donald Trump: He signed checks for people … and I didn’t.

At that point, the Democratic incumbent pointed to his head, and jokingly added, “Stupid.”

The trouble is, Biden raised an important point. Not about his intellect, of course, but about political strategies.

In March 2021, the White House touted $1,400 stimulus payments that were poised to reach millions of American families, but officials conceded that Biden’s name wouldn’t appear on the checks. The priority, the White House added, was to get the money out the door and into people’s hands, not to promote the president.

In hindsight, was that a political misstep? Probably. I remember talking to people who worked in Democratic politics at the time, and they were all baffled as to why Biden and his team weren’t focusing more on policymaking through a public relations lens.

Evidently, the retiring president has some regrets along these lines, too.

Trump’s obsession with self-promotion was cheap, exasperating and, at times, bordered on vulgar. But as my MSNBC colleague Ryan Teague Beckwith recently summarized, the political tactics “didn’t hurt” him then, either.

It’s tempting to reject cynicism and hope that the public sees through crass self-glorification, but while Trump has few redeeming qualities, the guy knows how to toot his own horn and capitalize accordingly.

In April 2018, Trump toured Mount Vernon and argued that George Washington was insufficiently focused on branding when naming his Virginia estate. “If [George Washington] was smart, he would’ve put his name on it,” Trump said. “You’ve got to put your name on stuff.”

Biden appears to have learned a related lesson, as has the rest of the political world.