Why are vaccines a successful treatment of allergy? As I understand the answer to Allergic rhinitis vaccine, the vaccine facilitates immune response against the antigen. Given that allergy is an overreaction of the immune system against harmless antigens, how can facilitation of the immune response act as a cure (moderate the response or so)?

The theory is that constant and gradual escalation of the administered dose of allergen eventually tolerizes the immune system to the allergen through the induction of peripheral Tregs or IL-10-secreting effectors.

While the purpose of a traditional vaccine against a pathogen is usually to rile up the immune system with and adjuvant or modulators, the idea of allergy immunotherapy is to sensitize the patient to the problematic allergen by implementing chronic exposutre. That mechanism is still poorly understand and is not thought to have immune memory, as the effects of the therapy tail off after discontinuation.