Right, the Eastern Church does not use annulment (or something analogous) because it allows remarriage anyway. If the Roman Catholic Church only looked at the canonical form it would not need annulment either. But we look at complicated cases, when the canonical form was present but the marriage was in some way flawed; for example, if an agreement existed to always use contraception, or to allow for adulterous affairs. It would be unfair to count such malformed marriages as binding.
Well, yes & no. We allow 3 marriages no matter how the first two end (been doing that for well over 1000 years; and while we do not have annulments, we do have, and require in the event that the separating spouses are alive, ecclesiastical divorces. Ecclesiastical divorces are not as easy to get as a civil divorce but it can be done by an exercise of economia by local hierarch.