A BST class is not impossible to be implemented. Nor should it not be implemented. However remember what Yoshi-P said? Due to that horrid plague that infected our world, a lot of projects were pushed back. Now given further time those projects might be renewed. But likely some will not. We've only seen two real BST class users. Lyon and Ran'Jit. And that was before the plague hit.

Also I still keep hearing people harp on BLU for reasons I don't understand. Why do people keep hating on BLU? Because it's limited? We've all seen how OP BLU can be. It can take over any role in the system depending on the skills chosen to be used. And honestly I like BLU for how it was introduced and how it may yet improve given TIME. The biggest problem the community is facing is people wanting everything they want now and the heck with what the actual creators are planning for us. The plague ruined a lot of things and yet people were fussing over SE still needing their subscription even though things would take longer. Remember that?

That being said. BST is still a possibility. My suggestions are as follows:
  • Find a gimmick for BST that makes it awe inspiring. The ability to merge with your beast's spirit and gain improved skill sets involving the partner beasts powers. Like Ran'Jit was able to do. You could use RPR void avatar possession skill as a base.
  • Find a tool or weapon that symbolically can be used with BST. Either a 1 handed Axe like in FFXI or something else. Shields are also a possibility that differ from GLD/PLD shields.
  • As for the beasts themselves make them not common ordinary beasts but majestic beasts like Dawon, or Gukelheinz. Beasts you don't find out in the environment but are tailored for the class. Beasts that rise in level with you similar to your Chocobo companion.
  • Another possible idea to implement is you can search out special beasts and fight them to tame them. Combine the aspects of a shaman and a BST and earn your beastly companions by connecting with their aetheric wavelengths or something that Garleans weren't capable of doing.