Why sameAs?
Avoids the asserting n squared triples problem
If you want to represent sameAs groups in a robust way, you need to assert owl:sameAs between all pairs from the group. Using sameAs, the system manages all that for you.
Does not create a new ID
The look up keys are all and any of the known IDs. This avoids the situation where the "problem" of too many IDs is "solved" by creating yet another one. See XKCD on standards.
Lifts equivalence management out to be managed separately, as it often has different
Facilitates distributed management
Knowledge management and creation are naturally distributed activities, concerned with multiple identifiers; the ID management needs to relfect this.
Facilitates collaborative solutions
Makes it possible to publish the data that was possibly only kept privately
Allows contexts to be captured by multiple stores applied to the same data
Facilitates deprecation of IDs gracefully
The system can be set to recommend a "canon" that creates a de facto agreed ID, and this can be changed to another ID, allowing graceful change to the new one, over time and place. Chosen IDs can be set to be keys, but not returned as results, thus giving the change a strong imperative.
Gives meaning to dead IDs
IDs disappear, while the things they reference don't, or they become deprecated. If you have one of these IDs, it is possible to find another, or a later ID to use and communicate with others, with the same agreed meaning.
Doesn't hold the labels/names
Having an equivalence management system trying to keep track of current labels is not a good thing to do. It creates a synchronisation and maintenence problem unnecessarily, since all the information about a URI should be available by resolving the URI.
Can work with differentFrom
There is another system differentFrom.org, that can work in tandem with sameAs services, to record the important information that an ID that might have been thought to be the same was in fact different.