Very interesting question @Cicero.
I would like to remark that the gradual extinction of vosotros started in western Spain, more specifically in cities like Cádiz, Huelva and Seville, all of them close to the western coast which has been an extremely important marketing route for centuries.
As a result, the Latin American Spanish is heavily influenced by these language variations (and many other variations like a similar pronunciation of the the letters s, c, z)
You might still ask yourself: Why vosotros is almost totally extinct in most of the Latin American countries? You might believe that it is used occasionally, in some situations but I can tell you for sure that, at least in México (25 years living here) that I have only heard latinos use vosotros like 3 times.
This is probably because of the cultural differences of each country, specially these key differences:
- The Latin American culture is highly hierarchical
You can notice this on business settings, when talking to a group of people with a perceived higher rank.
Muchas gracias a todos ustedes por asistir a esta junta. - Many thanks to you all for assisting to the meeting.
- Latinos way of speaking is very indirect, formal and non-confrontational
You can notice this on situations like accidentally bumping your shoulder with another pedestrian on a crowded street:
Ohh perdone usted, no lo ví! - Ohh sorry [you]. I didn't see you!
Or when challenging a point of view:
Me estás diciendo que estoy equivocado? [La contraparte responde] No para nada! Solo busco lo mejor para todos ustedes. - Are you telling me that I'm wrong? [The counterpart answers] No way! I just expect the best for you all.
Ustedes in turn is an abbreviation of "vuestra merced" which means "your mercy".
Vosotros comes from "vos" + "otros", almost literally "you all, the others"!
You can read the full story at the article EL USO DE USTEDES POR VOSOTROS
EN ANDALUCÍA OCCIDENTAL from the Universidad Autónoma de Madrid, it is quite a long essay but it explains this phenomenon very well.