The importance would be all the time and effort he put into it but know that he is dead he would have someone to take over
Even though synonyms generally share the same meaning, they might not apply in the same context. So, if you want to use one specific word you should do that instead of trying to find a synonym that doesn't quite fit into the context you've established. An example is if you want to use the sentence "I was mad", meaning "I was angry", you could look for a synonym. One synonym is "absurd". However, this is a different type of mad, meaning crazy instead of meaning angry. "I was absurd" has an entirely different meaning than originally intended. This is why you should always double check the contextual meaning of the synonym you want to use.
The first situation in which he used it to get himself out of a jam was when he was escaping from the cave in which he met smeagol, who we know is intensely aggressive when it comes to the ring. He slipped the ring on and it made him seemingly disappear. Another, much more trivial situation was when he bid everyone farewell at his birthday party basically as a show stopper (but also to avoid the judging eyes and boring personalities of his fellow hobbits).
The ring does not make Bilbo tougher, if anything, it makes him weaker. The power of the ring breaks him down mentally and physically.