The coded caching scheme proposed by Maddah-Ali and Niesen considers the delivery of files in a given content library to users through a deterministic error-free network where a common multicast message is sent to all users at a fixed rate, independent of the number of users. In order to apply this paradigm to a wireless network, it is important to make sure that the common multicast rate does not vanish as the number of users increases. This paper focuses on a variant of coded caching successively proposed for the so-called combination network, where the multicast message is further encoded by a Maximum Distance Separable (MDS) code and the MDS-coded blocks are simultaneously transmitted from different Edge Nodes (ENs) (e.g., base stations or access points). Each user is equipped with multiple antennas and can select to decode a desired number of EN transmissions, while either nulling of treating as noise the others, depending on their strength. The system is reminiscent of the so-called evolved Multimedia Broadcast Multicast Service (eMBMS), in the sense that the fundamental underlying transmission mechanism is multipoint multicasting, where each user can independently and individually (in a user-centric manner) decide which EN to decode, without any explicit association of users to ENs. We study the performance of the proposed system when users and ENs are distributed according to homogeneous Poisson Point Processes in the plane and the propagation is affected by Rayleigh fading and distance dependent pathloss. Our analysis allows the system optimization with respect to the MDS coding rate. Also, we show that the proposed system is fully scalable, in the sense that it can support an arbitrarily large number of users, while maintaining a non-vanishing per-user delivery rate.