In Marvel, there is a superhero team who's role is basically "clean up after the mess". Damage Control is a group of supers and civilians who are paid to clean up the mess and rebuild and fast. They apparently have an insurance arm as well, and superhero insurance is definitely a thing in the Marvel Verse. Marvel also benefits from the fact that most of the action is located in NYC, so it's probably a law passed to ensure buildings are insured against this, and within the recent story-line, the U.S. made it a law to register superheroes in exchange for legal protections and reimbursement for damages to property in pursuit of a bad guy. Runaways comics shows us that out in L.A. the Supervillain attacks are seen as an "East Coast thing" among L.A. residents (and the Supervillains steer clear of L.A. because an organized Supervillain gang controls that territory and put the fear of God into even the Kingpin!).
In D.C., it's generally seen that the JLA does do a lot of work to rebuild communities they break and some villains will do this too... for public approval. Lex Luthor and Bruce Wayne have public works projects to pick up damages for communities hit by these devastations. Obviously the former is generally met with suspicion by the heroes in the story, while the later is the primary funder of the Justice Leagues' cool toys, so naturally, Bruce has legitimate money going to side projects. At various times, it's often shown that the Justice League is all hands on deck when major damage is done to cities by their efforts to stop super-crime. Given that JLA members are generally more powerful than Avengers members, they tend to be the best at building things better than they were. There was one comic where Superman and Doomsday were fighting in down-town Smallville, the next issue picked up after Doomsday's defeat with the JLA on hand to build Smallville back up. Though the entire Superhero community of DC seems to have mad respect for Ma and Pa Kent. Over the years Superman wasn't the only superhero they couple has cared for, and Bruce Wayne is often seen as almost their adopted child.
This is also seen in shows like Justice League and JLU where the former usually featured 3-4 members of the 7 regular characters, and explained the others away as responding to emergencies elsewhere that were more natural disasters than actual superhuman. One episode even mocked this by explaining they couldn't dispatch Superman as he was handling Earthquake stuff in California, only for the Man of Steel to swoop in and block some more fragile member of the team from a devastating attack ("It was only a 4.0").
JLU would frequently show the heroes doing first responder styled work in the background during the conclusion of the episodes actions, or coming onto or off of shifts in the expanded Justice League. At least three episodes put these styles of missions as front and center, rather than background effects.
"The Greatest Story Never Told"'s central crisis is a deadly villain is on the attack and it requires as many heroes as can be mustered to fight, as told from the point of view of the heroes who were told they needed to do crowd control. It's widely considered one of their best episodes.
"The Doomsday Sanction" starts out as the Justice League assisting a Caribbean Island Nation in an evacuation as the local volcano is about to erupt, the real threat comes from the fact that Doomsday was accidentally released by the season's bad guys and single mindedly wanted to get his revenge on Superman, who was in the heart of the volcano trying to take pressure off so it wouldn't erupt.
"Flashpoint" was an entire episode dealing with the league doing some soul searching after a security breach knocks out power to their HQ and uses some of their own tech to absolutely devastate a community. The survivors are given some focus and the U.S. Government is showing some serious scrutiny of the League's culpability in the affair (though the President does recognize that the League has saved the world more times than he can count and are currently assisting in fixing the most immediate problem).
In fiction, these types of stories are generally not explored because it's boring, though anytime your superhero story starts exploring the need for heroes to unmask themselves, it results in this topic coming up.
Will Smith Movie Hancock did point out that Hancock's help does more harm than help, though one of the people Hancock saves is a PR guy and realizes that the devastation was inconvenient, but nobody was actually killed.
Pixar's Incredible works the public disgust at the aftermath into the setting with the public all but suing Supers into illegality (though IRL, courts do recognize that Life over Limb is preferable in a rescue situation, that is, if it's between breaking your arm or letting you die, a first responder should never let you die).
Similarly, the Captain America: Civil War film was about how do the Superheroes of the MCU account for the aftermath of there films (incidentally, it takes strong cues from the comic book government licensing system).
If this issue is not the crux of the work, in a more dramatic work, expect it to cause a lot of grief to the hero (and is critical to the themes of Spider-man) or is handled in a joking fashion (ala the entire concept of Damage Control, which is generally a humor series when it is in print or an aside gag in other titles in Marvel).