I’m confused by this–are you saying Dukakis really beat Bush? He lost by 7m votes in the popular vote and Bush won over 400 electoral votes.
I think if you look at history, 1932-1968 was an era of “Democratic majority/supremacy”, in fact something many argue to reflect this is that the sole Republican President in this span (Ike) was actually pushed into more of a Democratic position on lots of issues. In many ways, Ike’s win during this time is sort of an aberration and show show powerful the Democrats really were, Ike won because he was an extremely popular general, he would’ve won if he had ran as a Democrat too, and there’s good evidence people were voting for Ike the man not the Republican party.
After 1968, it’s been argued that we’ve switched into an area of “Republican majority/supremacy” that has since ended (albeit many argue about when it ended.) From 1968 to 2004 the GOP won most of the Presidential elections (68, 72, 80, 84, 88, 00, 04.) Their three losses come with pretty obvious explanations, too. Nixon was forced to resign for extremely corrupt behavior, Ford takes office and is initially there are some signs the country is ready to rally behind Ford after the scars of Watergate. Then very early in his term, Ford pardons Nixon, and is immediately accused of having made a “corrupt bargain” back when he agreed to become Nixon’s Vice President, to pardon him when the time came. We’ve never found out if it was true or not, but it effectively ended Ford’s political career either way. He almost lost to Reagan in the '76 primaries, and if he had, Reagan almost certainly would’ve beaten Carter.
As it was, Carter got in because of a unique situation, and he actually won a pretty close campaign against Ford–if Ford hadn’t pardoned Nixon or if Reagan had unseated Ford in the primary it’s really very likely Carter was never President. Carter was also helped (the same way Bill would be 16 years later) by being a Southern Democrat who was able to compete and win in Southern states–Carter actually being the last Democrat to actually carry the South, although Clinton was competitive in many Southern states.
Carter was quickly pushed out by Reagan, and we had another 12 years of Republican Presidents. Then we had Clinton win in 92 and 96, but his Presidency is very similar to Ike’s, but reversed. He was a “Democrat in a Republican time”, and to win he ran as a “Third Way” Democrat, which means adopting Republican-lite policies in many areas. He also was aided by a weak campaigner in George H.W. Bush, a somewhat fractured Republican electorate who were angered when Bush raised taxes (despite promising not to), and his reelection was aided when the GOP nominated a corpse to run against him in '96–a corpse that shockingly yet draws breath 20 years later.
Now, when this era of Republican supremacy ended is in dispute. Some view it as having ended in '00, with Gore actually winning the popular vote, and Bush is viewed as a “contra” President–a Republican holding office in a more Democratic era. I don’t take this view because Bush won pretty convincingly in 2004. I think that 2006 you started to see a real shift away from Republicanism as the dominant political force, and ever since then it’s pretty clearly been the “party of the minority.” (You’ll note I don’t wade into control of the House or Senate, because of issues like the power of incumbency, the crazy way we structure congressional districts and etc, the composition of the legislature doesn’t necessarily match the mood of the country–for much of the era of Republican supremacy there was actually a Democratic legislature, for example.)