I disagree. It's all about the money at the end of the day. The insurance companies get their cut with the monthly gun insurance fees. Just like car accidents, if the guns which are registered are misused in any capacity, the owner gets charged a higher premium (which nobody wants), especially if the gun is used in a mass shooting. This will make parents more accountable and teach their kids don't dare take the guns from the house and misuse it because they know it will hurt their pockets. Often times with these shooters, they operate on a solo tip. People will think twice if they know their family might have financial consequences for using a gun inappropriately, when they are gone.
When there is a price tag involved, people and companies tend to shape up very quickly.
To your point about making it easier for the upper class, I don't think that's relevant here because it's not individuals from the upper class going around committing mass shootings.