Skills vs. Tool Proficiencies
As you say, nearly all of the skill proficiencies function to improve a character's chance of doing something, but not to permit that thing.
Proficiencies that are 'gatekeepers' are more likely to be tool proficiencies, not skill proficiencies. As the PHB crafting rules explain (187):
You must be proficient with tools related to the object you are trying to create (typically artisan’s tools).
However, there is no artisan's tool associated with magic item crafting, and the core rules (DMG 128, 129) do not list a required tool proficiency to make magic items - only that the crafter be a spellcaster.
As NautArch points out, the requirement of proficiency in Arcana for magic item crafting proficiency is not a core rule, rather it is an optional rule that was added in Xanathar's. Given how Xanathar's expanded the rules for tool use, it isis odd that it chose to tie magic item crafting to skill proficiency in Arcana, rather than to invent something like an 'Arcane instruments' tool proficiency.