Across the country, Republicans are trying to choose a presidential candidate among four men they can't get very excited about, secretly wishing there was someone else. Here, one of those arcane arguments that excite the great and good of Washington is in full swing. It concerns an indubitably great Republican who served in the White House, and would be a perfect answer for his party's problems.

The fuss is over the planned memorial to Dwight Eisenhower, due to be ready in 2015 on a site close to the Washington Mall. Congress entrusted the project to Frank Gehry, responsible for, inter alia, the breathtaking Guggenheim Museum in Bilbao. Gehry's design calls for a park fronted by columns and bordered by 80-foot-tall metal tapestries depicting the Great Plains, and the modest home in Abilene, Kansas, where Ike grew up. His achievements as Supreme Allied Commander in the Second World War and then as the 34th US president would be illustrated in giant bas-relief.

Initial reactions to the proposal were favourable. Then the complaints began. The design, it was argued, placed too much stress on where he came from, and too little on what he did. Most galling, appar-ently, is the fact that the one actual statue of this towering 20th-century figure will show him not as general or president, but as a small boy.

The idea is reasonable: to convey "the dreams of a barefoot boy" that Eisenhower evoked in his speech to the citizens of Abilene in 1945, as the homecoming hero who'd organised the defeat of Nazi Germany. Because, he explained, "no man is really a man who has lost out of himself all of the boy". For critics, though, the concept is a travesty.

For what it's worth, I tend to agree. But happily, a wonderful new biography of Eisenhower has just appeared, reminding us just why a leader, long considered inept and out of touch and fonder of the golf course than in dealing with America's problems, is now ranked by many historians as one of the most admirable of modern presidents.

Jean Edward Smith in Eisenhower in War and Peace lauds Ike's role as Supreme Commander as he coped with the giant political egos of Roosevelt and Churchill above him, and the barely smaller ones of Montgomery, Patton and other subordinate generals. But it is Eisenhower's presidency that really comes into focus.

The accomplishments include the protection and expansion of social security, the creation of the interstate highway network, the founding of Nasa, and the racial integration of the military and of public schools. He ended the Korean War, and put a stop to the Anglo-French adventure at Suez. Yes, he made mistakes, such as his failure to take on Joseph McCarthy, the U-2 affair, and his support for the 1953 coup to overthrow Mossadegh in Iran which, to this day, stokes Iranian animosity to the US.

But after Korea, not a single American soldier died in action while he was in the White House. No one understands the horrors of war better than an old soldier; had he been president in 2001, Ike would have struck back at Afghanistan after 9/11, but he would never have blundered into a pre-emptive attack on Iraq.

Today, the Fifties have an imaginary golden aura of prosperity, simplicity and national concord. But part of that was due to Ike, as he took care to balance the budget, and work as smoothly with the Democrats in Congress as he did with the politicians and generals in the Second World War. And when he left office in 1961, he made that prophetic warning about the growth of the military-industrial complex, that now rings truer than ever.

Half a century after he left office, Republicans don't talk much about Eisenhower. Instead, they swear eternal fealty to Ronald Reagan. But what they surely need right now is another Eisenhower. Of course, he would be far too moderate for them – Eisenhower Republicans are as rare a species as One Nation Tories.

Wednesday saw what was probably the last 2012 candidates' debate. It was a real debate to be sure, but it did not break the pattern of this primary season – an insane stampede to the right, the quest to be the most perfect conservative of all, the insistence on a purity of faith St Ron himself could never aspire to.

Barack Obama is delighted as his opponents furnish quotes against each other that Democrats will use to devastating effect in the general election. And that's why there's talk of a brokered convention in Tampa, in which some dream of a new entrant (read Jeb Bush) riding to the rescue – even though Karl Rove, that unmatched reader of Republican tea leaves, says there's as much chance of this as of finding life on Pluto. That's why, if the hard-right social conservative Santorum wins the nomination, talk will grow of a third-party candidate, a deficit hawk who's moderate on social issues. That won't happen either. But if a temporary memorial to Ike belongs anywhere, it's at the entrance to the Tampa Bay Times Forum where August's proceedings will unfold.