First of all the fundamentals favored Bush with him being the VP of a popular admin, 64% of Americans thought the state of the economy was good(
https://ropercenter.cornell.edu/1988PresidentialElection) and more Americans thinking the nation was on the right track than wrong track similar to what those numbers were in 2000. While Gore lost a huge reason for that was he distanced himself from the popular president while HW did the opposite.
While some may point to the huge polling leads Dukakis had, remember in those days nominees used to get huge convention bounces so while Dukakis was probably still up till the RNC it was probably not by much either. Much of it was also cause of the perception people and the media created of Bush as being a "wimp" and someone who as only successful cause Reagan chose him but once his campaign proved that wasnt true , HW was gonna surge especially with the fact that the economy was on an upswing in 1988 as well(in 2000 there were signs it was starting to go down), and Reagan populairty was rising back throughout the year as well.
Lastly people forget how huge the Geographic advantage the GOP had then, basically Republicans were guarnteed at the very least to have this map
And states like Ohio were extremely difficult for the Democrats to win then too(Bush won it by double digits) and not every Dukakis state on that map was solid for the Dems either and threading this needle seems almost impossible. While a Democrat like Lloyd Bentsen could do it(by taking Texas and making the south competitive) , realistically he would have no chance at the nomination.
I think HW Bush as long as he ran a decent campaign was practically unbeatable in both the primaries and the general as even in the primary while HW might have been distrusted by conservatives, Dole was considered less of a Reaganite than HW was and while Kemp was closer to Reagan on policy he didnt have anywhere near the name recognition HW or Dole did and Kemp's FP ideology was gonna always hurt his chances and it did as he voted against the IMF Treaty