There isn’t a lot to go on from the question you have posed, but consider this.
If the fintech startup plans to do anything with fiat money, chances are it would need to be licensed and under this licensing umbrella, there will be a complete framework of how to handle risk, security, compliance, etc.
Whether the nodes are being installed at banks or not, remains to be seen as to what the solution may be, but banks don’t unilaterally allow others to establish nodes on-premise.
Banks have to work within a very restricted elbowroom, (read: strict framework).
To answer your question, so is it smart for any fintech startup to develop an distributed ledger application that will target the bank’s audience – not sure. May be smart or extremely dumb, depending on the idea.
Would installing nodes on bank’s premise be a major security concern? Well it all depends on the acceptance of that node by the bank’s risk, security and compliance teams. Not to mention, the regulator’s nod on allowing such a node to be present.