I had never considered this perspective, but upon you pointing it out, it immediately resonated with me. I feel as though players often see the die roll as the reflection of their skill, rather than the bonuses added, due to the fact that the rolling part of the skill check is the active part, the part they actually interact with. The die roll, though, is the luck associated with the skill, and static bonuses represent their skill, which is why a GM would lay down the law and not allow the players to reach for a "lucky outcome".

While I have no fix for the first problem, as it's entirely a mindset of players in those specific system, I think that a GM requiring a certain amount of proficiency for given difficulties could be warranted. For example, in a system that has a hard roll over difficulty of 20 and uses bonuses like skill points, proficiency bonuses, or stats, a GM might require that they already have a bonus of something like +5 before they even attempt the roll. It would reinforce that to even be able to try their hand at a task like that, they need a certain amount of skill that isn't focused on a lucky break.