I spent some time reviewing resources related to this online and was unable to find anything comprehensive. I think at best we'll have anecdotal evidence to support any answers.
Speaking from experience I believe loading screens are influenced by your character level; they are also influenced the locations you've visited and milestone's you've achieved. For instance I did not see any loading screens related to Goodneighbor until I actually visited the location. Likewise, I did not see loading screens with information about assualtrons and sentry bots until my character was higher than level 30*.
However, I do not believe that loading screens have a maximum level they appear to the player. Rather, as your character levels up and achieves more milestones more loading screens are added to the loading screen pool and you are less likely to see existing screens. They don't disappear entirely, they do appear less frequently.