If I want to use money to pay for some goods, I need trust that I can get that money back if the goods won't arrive. Math alone can't provide that, it needs something extra, e.g. a trusted escrow service in the case of crypto.
If I want to use money as a store of value, I need trust that the value is going to stay stable and maintain liquidity in the long term. Math alone can't provide that, that trust is inherently social. I also need reasonable trust that the money isn't likely to get stolen - math isn't sufficient for that, and our current experience shows that crypto assets are more vulnerable in practice than e.g. bank deposits, maintaining appropriate "opsec" is tricky and people fail in that too frequently.
And for your other point, the economy existed before a monetary system and currently works off of many monetary systems - however, for a monetary system the only criteria that matters is if it's good for what the economy needs; if some system does not fit these needs, then it won't get used much and is not particularly relevant.