I don't consider myself an expert here, but I believe there are few or no problems that only blockchain technology can solve. Rather, it's about
how it solves problems.
If you solve a problem with non-blockchain technology, you will get a centralized entity of some kind. Be it a bank, a SaaS service, a social network, a database, or whatever. Sure, it can be open source, but it's still centralized in one way or another, and decisions must be made be someone. If you are the owner or have privilidged access, you may do bad things (alter data, abuse user data, increase prices, etc).
With blockchain technology, you can get around having a centralized entity. Instead, you are developing an incentive schema that allows distributed ownership and decision making, so that all participants have power and are incentivized to behave in the best interest of all.
Besides money, there are many other cases where this make sense, but is the downside of having a centralized entity really large enough to justify the downsides of blockchain (hard to develop, slow, hard to use and manage, etc)? Probably not right now, and maybe it will never get to the point.
IMO, a well-run, transparent, centralized entity can be more trustworthy than a complex technology that is potentially exploitable, buggy, you don't fully understand, and is difficult to change once to initial incentive schema is in place.