When I used to travel frequently, I had 2 UK passports.
It was still possible to end up in one country with one passport, whilst the other was somewhere else getting a visa.
The answer then, and now, is that is exactly what couriers do remarkably well. DHL was founded to send documents around the world, (for the shipping trade), and it excels at it still.
All the fine theory in this thread was not going to work. Only couriers could fix the issue.