It makes sense that because the same teeth are running over each other, an imbalance (ie a teeth wearing more suddenly than the rest) will be made worse quicker over time. That happens in an evenly divisible teeth configuration I believe like 10/40. But in an odd configuration, say 11/40, the teeth that are running over each are rotated around. This helps spread the wear if there is any.
Pulley
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Motor
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
In this even configuration 3/9, 1 will always mesh with 1,4,7. 2 will always mesh with 2,5,8, and 3 will always mesh with 3,6,9. Say 1 is a bad teeth, it would cause even wear only on 1,4 ,7.
Pulley
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Motor
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7
In this configuration 4/9, you can see 1 getting meshed with every other teeth so if 1 is a bad teeth, it would evenly wear with the rest of the teeth.
I understand the concern for this in applications with high rpm/load but I am curious to see if it applies to eskate gear drives.
edit: for grammar and wording