The only difference between a normal aeon and the Final Aeon is the way they are obtained. Normally a summoner would go to a temple and pray to the fayth. For the Final Aeon they go to Zanarkand and have one of their guardians turned into the fayth. Usually these fayth aren't sealed into statues as they are used to fight Sin and become the next incarnation. In Anima's case Seymour decided not to accept his mother's fayth, so she was sealed away so her sacrifice didn't go to waste.
The summoner doesn't merge with anything. The guardian is turned into the fayth of the Final Aeon which is given to the summoner. Usually the summoner then faces Sin and calls the Final Aeon. The aeon defeats Sin and then is absorbed by Yu Yevon. The process of Yu Yevon joining with the aeon severs its ties with the summoner, killing them. As they are only used once there is no need to have a statue dedicated to it.
The exception is Zaon. He and Yunalesca were the first to fight Sin so their feats are commemorated.
Zaon's statue is empty because his soul is now at the bottom of the Via Infinito.