Does receiving deliverance rites mean going directly to the Western Pure Land of Ultimate Bliss?

Not necessarily. Receiving deliverance rites does not mean every deceased person goes directly to the Western Pure Land of Ultimate Bliss. I often compare it to studying abroad. To attend an ideal university, besides someone helping with arrangements, your own level and preparation need to be sufficient. Wanting to go does not mean you have already completed your studies and graduated.

In this comparison, merit and blessings accumulated during life are like travel expenses. If these are insufficient, family members can perform meritorious acts and arrange ceremonies, asking the deities and Buddhas to help. If the person's level is not yet sufficient, they might first be placed in a better language school to keep learning before moving toward the desired destination. Family members add support, but the person still has to do their own learning.

In my understanding of faith, deliverance means doing our best to address the person's needs at that time and help them reach a better place. Deities can help arrange things, but whether the person proceeds smoothly afterward still depends on their own abilities, conditions, and blessings. The time needed to learn there is not the same for everyone. Receiving help from deities and Buddhas does not conflict with still needing to learn for oneself.