I think you are not understanding how bitcoin works, and this exact problem of double spending was better solved by bitcoin. You dont need to trust a third oarty or “online service”, you can dimply run a bitcoin node. If it is that important a raspberry pi and SSD is cheaper than your average credit card terminal.
The credit card network, by the way, is much worse in this regard.
...so you need to be online, connected to the rest of the Bitcoin peer-to-peer network, to engage in a transaction. I am talking about offline transactions, where I only need to communicate with the other party in the transaction. Again, you can just read the paper I gave a link to, which describes this scenario, or any of the other hundreds of papers published on the topic.
Unlike many great ideas, those in the paper you cite just haven't yet gathered enough acceptance.
The value of the US dollar as a reserve currency is a faith-based article, and yet it works well. The confidence in the Fed to not unduly dilute the value has reinforced the resolve of the participants to continue to accept it as currency.
Bitcoin's paid many years of dues in this regard as well, and its garnered the confidence of its market participants despite its deficiencies.
The credit card network, by the way, is much worse in this regard.