There aren't really any prominent conspiracies about the John Hinckley Jr. shooting; people, even those prone to paranoid thinking, just see him as a weirdo who failed rather than some CIA lackey. Had Reagan actually been killed though, that wouldn't have happened, you'd have Alex Jones outright linking to Taxi Driver to MKUltra. So I think a failed Kennedy assassination would have a similar effect on the public conscience. Oswald would be seen as a Hinckley type, a crazed lone gunman, rather than part of some vast deep state conspiracy.