Here in Western Africa I have come across such an example. In the interest of personal security I am going to mask a few of the details but believe me this is a true story.
An African national who lives in the US with his family, and therefore has a Green Card, is currently working in Africa. On his way back home later this month we planned for him to stop off in London for business meetings at Head Office. He needs a visa to visit the UK which we thought would not be a problem. However, the first step would be to apply for the visa at the UK Embassy in another African country. If approved he might be required to travel there for an interview. The application then goes to another UK Embassy in East Africa where processing could take between 4 and 5 weeks. Given that he is a citizen of yet another African country (that's four if you're counting) this is getting seriously complicated.
I often complain - to myself - about the cost of visas to visit and work in Africa but to be honest the situation is far worse for Africans wishing to visit Europe or North America. I have heard of another example where the Canadian Embassy has held a passport for 5 months with no end in sight.
For all the talk by the politicians about helping Africa, doling out billions of dollars in aid that seems to disappear or is linked to sales of expensive infrastructure that plunges economies into debt, the opportunity for Africans to visit and benefit from what so-called developed countries have to offer has been abandoned.
And the most ironic aspect of my story is that the person involved received part of his higher education as an engineer at a British polytechnic.