Giving a strong (either affirmative or negative) answer to questions like "is X useful to build secure systems" is hard. Basically, because what secure means depends on the specific use case and because you could find intrincate ways to achieve security.
For instance, if, for a given system being secure means ensuring information confidentiality (as in confidentiality of an encryption), then basing such system on a blockchain does not seem to be a good idea.
But also, blockchain systems do not seem a priori useful for building a system that allows performing private computations. But then, take Baum et al paper "Publicly Auditable Secure Multi-Party Computation." It describes an MPC system that uses an append-only bulletin board. This is precisely the idea that triggered the Enigma blockchain-based system, which provides secure multiparty computation using a blockchain as the append-only bulletin board mentioned in Baum's paper.
And, if you want to take things further, it has been shown by Ishai et al that certain types of zero-knowledge proofs can be built from MPC too (disclaimer: I have not studied Ishai's paper, so I don't know whether or not a blockchain-based MPC system like Enigma's would be a valid implementation for its specific construction, but this serves me to make a point.) Now, zero-knowledge proofs are one of the most used cryptographic primitives to build secure systems. Probably, using a blockchain to build an MPC to then build a ZK proof to then build some other secure protocol is way far from efficient. But there may be variants or special cases for which it is still useful (and at least, from a theoretical point of view, seems very interesting.)
Also, just quoting the abstract of a very recent paper, "SoK: A Consensus Taxonomy in the Blockchain Era," by Garay and Kiayias:
Consensus (a.k.a. Byzantine agreement) is arguably one of the most
fundamental problems in distributed systems, playing also an important
role in the area of cryptographic protocols as the enabler of a
(secure) broadcast functionality.
Now, blockchain systems can be seen as a special type of consensus systems, where security is defined (in the referenced paper by Garay and Kiayias) in terms of termination, agreement and validity properties. Therefore, a blockchain system can be used to implement a secure broadcast channel. So this is another counter example of blockchains being useful to provide some specific type of security.
To summarize, there may be non-intuitive ways to achieve security and, moreover, what does it mean for a system to be secure depends on what are the properties that such system needs to ensure. Confidentiality may be one, but there may be a lot more, as some of the other answers have pointed out too.
PS: This said, sure, there is way too much hype and too much people trying to use blockchain everywhere without making sense of anything.