You don't want to distribute the production too much. Doing it massamuusi's way it takes 5 years to produce a fully buffed unit and what happens if one of the provinces is invaded? Even if for only a turn the Churches could be destroyed if the invaders are Muslim or Orthodox.

Even if one of the provinces is not actually invaded but a neighbour becomes an enemy then you are likely to keep troops in the border province and the cycle will be broken.
And also if one of your provinces is not coastal but inland there may be another year or two required to get the unit where it is needed.

Sometimes that can't be helped, but using 3 provinces to build one unit type is very inefficient and as ConstableBrew pointed out after the first few years building the buildings in each province for the lower end units would speed the process up. It is not as slow as he says though because he forgot that a second group of 3 could be built on year 2 when the first group was moving and that would mean 6 every 7 years and a circle is not the best method anyway.

A better way would be a production line Starting with one unit in Province A and then moving on up and would give you one fully buffed unit every year after Year 4.

A few notable exceptions exist mostly to do with the valour bonus provinces. There are other also but some examples are :

*Chivalric Knights from Toulouse could be retrained in any of the Iron provinces for Weapons upgrades.

*Turcoman Horse Archers can be easily trained to V2 in Tripoli and then retrained, allowing Tripoli to get its farming and trade buildings working.

*Almohad Urban Militia can be trained V1 in Granada an then buffed in Cordoba, or not if they are to be used in the Desert.