Sometimes people resist fixing serious issues with a legacy system, because rewriting the legacy system is seen as preferable to evolving it. But, the rewrite always takes a lot longer than you expect, which can result in a lengthy period in which those issues continue to bite you. Just hire a few good mainframe COBOL programmers (they still exist) and fix the serious issues in the legacy system.

Changing a legacy mainframe COBOL system shouldn't be scary. Provided you have qualified staff and the right tools (such as COBOL static analysis tools), it is not inherently more risky than changing a Java or .Net app.