This paper investigates the potential contribution that interconnectors can provide to efficiently support the security of interconnected power systems. The proposed modelling setup introduces a radical paradigm shift in the operation of the interconnectors and in their interactions with multiple markets. To the best of our knowledge, this is the first paper that models a simultaneous allocation of the interconnector capacity for the exchange of energy and of inertia-dependent primary frequency response. The benefits and impact of this new methodology are evaluated with typical market indicators (e.g. social welfare and interconnector revenues) under two different paradigms: a centralized approach where the interconnectors are operated to minimize the system operational cost and a market-based framework where the interconnectors are privately-owned assets with self-interested objectives. By modelling the interconnectors as price-maker, the proposed work quantifies the potential inefficiencies of market solutions while considering key elements such as capacity withdrawing. A case study of the GB-France systems assesses the value of interconnectors on system efficiency and security under the considered paradigms.