Strictly speaking, ICAO does not require aircraft operators to prepare a safety case; only to use a safety management system. Some may argue that this inevitably will result in a safety case of some sort, but it is not required.
You ask why operators do not prepare safety cases. I don't work in flight operations (but in ATC) and my experience would suggest such documents or arguments are seen as providing little benefit. Regulators are not skilled in using safety assurance documentation as a basis for oversight. Often the regulator seems to use 'Send us a safety case...' as a means to avoid a having to make a decision, and then, when it receives a safety case, doesn't know what to do with it.
From the service provider's perspective, safety management seems to be yet another opportunity for the few skilled (and semi-skilled) safety management practitioners to sell their services, and write a pretty document that no-one in the SP reads, or understands, or believes in.
Do I sound cynical? Maybe it's because after 10 years I've seen lots of SMSs, and quite a few safety cases - heck, I've even written some - but all we seem to have done in the vast majority of cases is produce piles of documents with very little demonstrable improvement in safety. And, in most cases, good, experienced, professional decision makers can still knock spots off someone who is given the job of 'looking after the SMS'.
Want to fix it? First, start by getting the regulators to understand how a good SMS will work and what a safety case really is; second, get them to explain what they need to the operators.
And the (admittedly limited) exposure that I have had to SMSs/safety assurance in other industries suggests to me that effective implementation is patchy at best and is handled by the respective industries in much the same way as it is in aviation today. I'd be glad to be shown to be wrong because I'm a believer in the SMS approach, but I'm yet to be anywhere near to being convinced.