At the beginning of the Seder we invite those in need to join us in eating Matza and the rest of the Seder. But what kind of invitation is this? Its a bit late to be inviting people to the Seder, and besides if we say it at our house no one is going to hear us anyways. (Furthermore, in the time of Korban Pesach, guests could not be added after the Pesach was slaughtered).
Perhaps this is acting as a retroactive invitation. It is very awkward to invite yourself to someones Seder. However, once it is common knowledge that every host makes a general invitation to the Seder, then to let someone know you want to be a guest is not inviting yourself, rather it is accepting a future invitation which you know is coming. Once the guests have arrived, making a welcoming invitation helps serve to make everyone feel comfortable.