If you go with the "do something" in each country theme (not just clear immigration, step out the airport door and see the sky, go back through immigration and back on the plane to another country) then it could take a while. If you stay overnight in each country, then obviously at least 200 days or however many countries there are.

On item is what country are you from? Which citizenship has the most visa waver agreements in the world? If you want to do a nonstop trip, then even for a US citizen to get all the visas in advance would be a major undertaking. Having to send your passport and extortion $200 to all the embassys in DC and waiting 3 days each even for expedited visa would be a chore. If your visas are good for 6 months your trip better take less time than that.

Other travel problems: Does your trip time include the stop back home? If a US citizen goes to Israel, won't they have to come home, have their "dog eat their passport", then get a replacement expedited before they can travel to certain Arab countries? Certain nationalities (Swiss? Singapore?) might have an easier time or fewer visas.

Other question: Do these have to be legal visits? If a US citizen does a MR to Cuba does it count?

So many questions.