Inflation may have stayed low in recent years simply because independent central bankers are good at their jobs. Increasingly independent central banks helped lower inflation rates around the world.
This is one reason economists have expected low inflation while central banks printed money. Quantitative policy works if run in a politically neutral way. An independent central bank tries to match money demand and money supply. The surges in money demand after 2008 justified money printing.
Central bank independence varies. The European Central Bank's independence is guaranteed by treaty and the lack of a euro area government. The US Federal Reserve (Fed) has a different independence; much depends on personalities. Arthur F. Burns, the Fed Chair in the 1970s, operated in the same institutional framework as Fed Chair Janet Yellen. Fed Chair Burns used to consult President Nixon about where interest rates should be set.
US President Trump can now appoint four Fed governors (of seven). Trump could nominate a fifth governor if Yellen is not reappointed Fed Chair and chooses to resign as governor. The Fed has put quantitative policy on "automatic pilot" by preannouncing the path of reduced money supply. However, the precise path of monetary policy is less easy to determine when so many personalities are unknown.