Did Gothamites have to love Batman during BB so that we could accept the premise of TDK? I think it's a dumb argument to claim that forwarding the story by a certain time without showing that passage of time reduces the value and quality of the sequel's story. TDK happened like what a maximum of 1 year after BB and the movie explicitly showed that Batman was both loved and scorned by people, which is a template followed by BvS. We didn't even get to see him become this beloved hero that the police trust, only through dialogue and quick establishing scenes. Yet we accept the premise of TDK. The movie is also considered the greatest in the genre too.
The way I see it, the parallels of Nolan and Snyder are quite similar, though a bit different in execution, but nevertheless similar in both structure.
BB - ends with Batman saving Gotham
MoS - ends with Superman saving Metropolis and Earth
Time skip:
BB to TDK - Months to a year
MoS to BvS - 2 years
TDK - Batman is both a beloved and hated figure as shown in the establishing scenes
BvS - Superman is both a beloved and hated figure as shown in the establishing scenes
The time skip in BvS was done flawlessly by retconning Batman as a 20 year veteran. MoS2 is not necessary before a Batman and Superman story, a versus or team up movie, but it can be done anyway.