To your first question, trust is only established or maintained from the user to the software application. There is no requirement to trust other people or organizations. Trustless applications and softwares requires a pretty complicated software development process, however it is already possible. You can check out some dApps here: https://www.stateofthedapps.com/.
The concept of disintermediation through blockchain was first a proof of concept published by the Ethereum foundation. The concept is fairly simple, instead of a central intermediary organization that requires a workforce, hardware, and other assets that introduces some form of friction in the market, why not just use a “smart contract” that facilitates this regulation.
So in the case of Taxi disintermediation, if I was a Driver and wanted to register I would simply need to submit my drivers license and maybe other car documentation. The smart contract can access public records, ensure all the details are correct and that the driver is not dangerous of any sort. The rider would simply be connected to the closest/available driver through the smart contract algorithm. Now what about the 5–10% of the times when something out of the ordinary like an accident or someone's money disappears in the app, who can I contact to get things fixed?
So this is where it gets a little interesting, Ethereum thinks of its network as one big global computer. Where smart contracts can interact with each other independently. For example if you get into an accident the smart contract can connect with other smart contracts in the ethereum ecosystem that may facilitate emergency services, if you lose your money maybe a smart contract that’ll connect you with a blockchain analyst who can figure out where your money’s gone, or maybe a contract that takes you to an insurance company that will cover your lost funds. As a Solidity developer, all of this is definitely possible but right now I doubt there is enough infrastructure in the network to implement such things efficiently. At this point though there are companies tied to dApps that you can contact and get support from, but these companies don’t process transactions.
However, nothing from the user interface perspective would actually change for both the driver and rider, its the business model that radically changes. This is happening with open source apps and games right now, where majority of all dApps(decentralized apps) are all being tokenized with an underlying currency to facilitate transactions. The more transactions happen in the network the price of the currency will appreciate. The developers and/or the organization that developed this dApp holds 20–30% of the total supply of tokens. Generating a profit through price appreciation. With this new business model the users would maybe pay some minor network fees 1/10 the current price. Meaning this reduces friction costs, equalizes profits between all users
I however agree, this concept of disintermediation will only be useful in some use cases, we cannot assume it will fix every industry. But due to the lack of current blockchain infrastructure, we really don’t know how far the concept of disintermediation can take us. Im sure 20 years ago we never assumed the use case for companies like Netflix, Uber, Airbnb, Facebook etc.. would ever exist.