You're free to state your preferred definition or if you don't like any possible existing static definitions, that's fine too. Lots of good people make up definitions in mid sentence. I find it less work to use the definitions from U Mich, they serve well when working in financial careers such as mine. I can understand how someone else could define wealth as anything they want just to win an argument. I find it too much work to switch definitions when going from work to worship or home.
I don't think when discussing saving that the definition of wealth should be structured so that it can hide debt in excess of assets held.