It's a great idea, but only can work in a revenue sharing model - otherwise, touring teams would like to use that time for exchanging bi-laterals. In most countries, Cricket is a dying sports, hence hardly any neutral (matches not involving hosts) match is commercially viable, unless it involves IND. Only way a neutral match can have financial positive is involving IND, therefore even the best triangular (WSC) was closed after 2005-06 season & the Triangular format only returns those years when IND tours that year. UAE was another great neutral venue - died in few years time when IND decided not to tour.
In recent times, apart from WSC, I think, I have seen one Tri Series in WI (Again IND was one of the 3 teams) & this one in ZIM. We'll have to understand that the Cricket market is dominated by South Asia, particularly IND; hence only way a Tri (Or more than 3 teams) Series is possible in places where there are lots of Asian crowd - most where, Indian crowd out numbers the host these days. But, it'll not work in IND without PAK being one team, because the neutral matches won't have any appeal; might not work in AUS, NZ & SAF as well without IND being one team. Only places, where a Tri series can work (Excluding UAE) is probably in ENG, BD and ........ may be Canada (Toronto) - provided that, 2 of IND, PAK, SRL & BD are 2 teams of the 3.