In previous Elder Scrolls games, each character had access to every skill. The issue I had with this was at high levels, every character was essentially the same. In Oblivion and Morrowind, when a character had 100 in every attribute, and 100 in every skill, there wasn't a significant difference between a Nord and a Breton.
The different classes in ESO give a distinctness to each character. However, there are only four character classes, which doesn't create a lot of variety. To allow for greater variety among the classes, each character could gain access to one cross-class skill, starting at level 10n. Access to cross-class skills would effectively increase the number of distinct classes to 36, giving players greater flexibility in creating their characters, while maintaining the integrity of the four base classes.