Grace Hopper did not invent COBOL
COBOL was ultimately designed by a committee, but Grace's early compilers had a lot of influence on the language design.
The military and other organizations found it difficult to build financial, logistics, and administrative software for multiple machines that each speak a different language, and thus formed a joint committee to create a common language. (Science and research institutions had FORTRAN for cross compatibility.)
Basically the COBOL committee grew sour with disagreement. As the deadline for the first specification approached, the committee fractured into a "git'er done" tribe, and a "do it right" tribe. The git-er-done tribe basically cloned Grace's language with some minor changes and additions because they knew they didn't have time to reinvent the wheel from scratch. Grace's language was road-tested.
As the deadline came up, the git-er-done group were the only tribe with something close to ready, and so that's the work the committee heads ultimately submitted. There were a lot of complaints about it, but the heads wanted to submit something rather than outright fail. (The story varies depending on who tells it.)
Later versions of COBOL borrowed ideas from other languages and report-writing tools, but the root still closely mirrored Grace's language. Therefore, it could be said that Grace Hopper's work had a large influence on COBOL.
(It's somewhat similar to the "worse is better" story between Unix/C and a Lisp-based OS: http://dreamsongs.com/WorseIsB... )
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As far as what orgs should do about existing COBOL apps, it's not realistic to rewrite it all from scratch, at least not all at once. That would be a long and expensive endeavor. It's probably cheaper to pay the higher wages for COBOL experts, but also gradually convert sub-systems as time goes on.
However, whatever you pick as the replacement language could face the same problem. There's no guarantee that Java, C#, Python, etc. will be common in the future. Rewriting COBOL into Java could simply be trading one dead language for another.
I know shops that replaced COBOL "green screen" apps with Java Applets. Now Java Applets are "legacy" also. (And a pain to keep updating Java for.)
Predicting the future in IT is a dead-man's game. At least the COBOL zombie has shown staying power. If you pick a different zombie, you are gambling even more than staying with the COBOL zombie.
If it ain't broke, don't fix it. If it's half-broke, fix it gradually.