Washington (CNN) President Donald Trump's selection of former Republican presidential candidate Herman Cain and former Trump campaign adviser Stephen Moore to fill two open seats on the Federal Reserve board has unleashed a wave of anxiety about the independence of the world's most powerful central bank.

But even if they were to make it through Senate confirmation -- an uncertain outcome, given bipartisan objections from senators that have surfaced even before either has been formally nominated -- neither Moore nor Cain would have any immediate sway over the seven-member Fed board of governors.

Though they would likely inject additional turbulence and uncertainty, offering splintering views in speeches and interviews, they would be in the minority when it comes to policymaking, outnumbered by traditional bankers and economists aligned with chairman Jerome Powell

The seven-member board is already dominated by people chosen by Trump. The President has made three appointments since he assumed office in January 2017, all of whom were confirmed with bipartisan support, and chose to elevate Powell, originally an Obama appointee, by naming him chair of the board of governors in 2017.

Only one other Obama appointee, Lael Brainard, remains -- and her term runs through 2026, after the end of a possible second Trump term.

A Fed governor can be nominated by the President for a full 14-year term, and cannot be removed from office except for "cause" -- which does not include their policy views. The length of the terms mean governors routinely outlast presidents, and the terms are staggered to further insulate the Fed from political pressure.

However, nothing requires a Fed governor to serve out their full term, and many don't. That means new governors are often appointed to complete the balance of an unexpired term.

One Trump appointee, Michelle Bowman, comes up again in January 2020 -- the last Fed seat to open up before next year's presidential election.

Three more seats are due to come up in the next presidential term. That means that if Trump wins re-election, he could put his stamp on the Fed well into the 2030s.

And, more importantly, he will be in a position to name a new chair in 2022.

Trump's unprecedented attacks on the Fed

Since last year, Trump has publicly ripped into the Federal Reserve, calling the venerable institution filled with the country's top economists as "crazy" and "loco" for raising rates four times last year under Powell.

He's even gone so far as to threaten firing Powell , Trump's own choice to lead the central bank for a four-year term that expires in 2022, claiming that rate hikes have undermined his plans to drive economic growth.

Powell, a former investment banker who also served in the George H.W. Bush administration, was initially appointed to the Fed Board by President Barack Obama but named chairman in 2017 by Trump at the urging of Treasury Secretary Steven Mnuchin, succeeding Janet Yellen.

During his tenure, Powell has repeatedly defended the impenetrability of the Fed to political interference, telling an audience in January, "We have a strong culture. It's not a fragile one. It's not subject to be being disrupted."

So far, Powell has been able to build consensus with his existing board, with not a single dissenting vote on any policy decision since he took the helm in February 2018.

That would change with Moore and Cain on the board.

Private dissent is common on the Fed board

It's not rare for members of the seven-member Board and any of the 12 regional Fed presidents around the country to offer dissenting views on monetary policy, and Fed chairs -- at least publicly -- have embraced diversity of views as a tenet of policymaking.

Members of the Federal Open Market Committee, comprised of the seven Board members and 12 regional Fed presidents, have dissented under both of Powell's predecessors. Janet Yellen garnered 22 votes in opposition across a total of 31 interest-rate setting policy meetings while she was chair and there were 58 dissents under Ben Bernanke's chairmanship over the course of 65 meetings under Presidents George W. Bush and then Obama.

But any perception of undermining the independence of any central bank runs the risk of undermining its effectiveness at keeping the economy on even keel and preventing inflation from taking off.

"The potential nominations of Herman Cain and Stephen Moore suggest the administration is changing its approach to the Federal Reserve," Michael Gapen, chief US economist at Barclays Investment Bank, wrote in a note clients. "The selections could raise questions about the independence of the Federal Reserve and could be perceived as an attempted politicization of monetary policy."