Surprised to see so much misunderstanding here. “Byzantine fault tolerant consensus” problems have been solved with a trusted party since many many centuries. Entire modern monetary system is based on a trusted party - a central bank. Blockchain provides a way to remove trusted party out of equation. One can argue that existing system just works, why would you want to change something that works? Answer is simple - it does not work in many countries and trusted parties/authorities abuse their powers, sometimes in a ways that is not so easy to see.
First application of a blockchain is digital money which is free from a central authority. Here is real world scenario that happened in so many places. Your domestic currency is crushing, has lost 30% of it value already and is about to loose another 80%. You want to by US dollars and save what is left but you cannot because government temporary prohibited purchase of a foreign currency. I’m thinking about Russia, Belorussia, Venezuela and many many others.
Political activists get blocked by a banking system all the time. For example in Russia there is a “list of terrorists”, people on this list excluded form the banking system. This list probably has some terrorists in it but it also has quite a few activists in it as well. You can go to a protest, grabbed by a police and next day find yourself out of the banking system.
Decentralized money is at least partially a solution to issues arising form an authority abusing it powers as cryptocurrency cannot be blocked so easily. It does not have to be used much, it just has to be around.
Second blockchain application is smart contracts to simplify value transfer. For example shares offerings - when a company sells it shares to a bunch of investors. It often happens outside of an exchange, without IPO (search for Reg-A, Reg-D offerings). In this process a bank holds investor money until offering completes and a “transfer agent” hold stock in the name of an investor after. Bank and transfer agent are there only because of trust issues, someone has to guarantee that investor pays and receives shares. Investor cannot directly hand over cash to a company because it can fail to pay or company can fail to deliver it shares and then they will have to spend time and money in court. Both bank and transfer agent take their commission just because they trusted and licensed to hold value during and after transaction. These commissions are not small, a bank may take few percents for organizing an offering.
Shares can be issued on a blockchain and a smart contract can govern entire value transfer starting from escrow, to enforcing offering conditions and then to transfer of shares and money to counter parties. You can imagine banks might not be happy about loosing their profits but competition in democratic countries slowly but surely drives process in a right direction.
Similar examples arise all the time in international trade, trade clearing, interbank relationships, etc, etc. blockchain is a solution to all of this but maybe we need another financial crisis (when “trusted parties” became not so trusted) to speed up it adoption.