Latest reputable polls in each of those states suggest your information is incorrect, per 538 and their polling grades.
NC:
Emerson has Trump +2
OH: Polling has been weaker here than other "battleground states" but
Morning Consult has Trump +3
GA: This one is actually split so if you were ever going to make the case you're trying to make, it'd be for GA.
SurveyUSA has Biden +2 and
Monmouth has Trump +1/+3 depending on Likely vs Registered Voters
I'd also wager that the VP pick mattered significantly in terms of visibility and demographics but didn't matter at all for picking between Biden and Trump. If you don't vote for Biden now because he picked Kamala Harris as his VP, you were never going to vote for Biden anyway. And as I said above, if we are talking on November 3rd about whether Biden is close in OH/GA/NC, the election is already won.