Would it be possible to expose a system configuration option that would enable an organization, if they choose, to enforce that any newly created custom field always be assigned a project-specific context and to automatically delete the global context?

This would never stop a custom field from being reused.  You simply add another project-specific context.

But this would stop the sprawl of custom fields into field configurations across all projects in a Jira instance, and would lessen the probability that, with the creation of each new custom field, we necessarily make Jira slower for everyone.

Because unfortunately not every organization has a dedicated Jira admin or set of admins that force the reuse of custom fields and actively prevent or discourage their creation.