no...it is in no way lifeless...you are unable to mark this bitcoin system as useless right up until the total coin exhosted from the market and no one particular accepts it any longer or you can say it losses its values and respectvin the economic system
What are you even saying ?
First, before we get to that point of the whole bitcoin being mined, do you know the value it would have been worth by then and the fact that it is limited and it has a lot of value and usage is what would keep making it increase in value over time.
People will keep accepting it, those holding it, would start exchanging as payment means and for buying stuffs and the real life usage would have become something pretty much cool than just holding as an asset.