At previous job, we had migrated from a nasty cron orchestration system to jenkins. It did a number of things including building software, batch generating thumbnails and moving data about on around 30 nodes, of which about 25 were fungible.
Jenkins job builder meant that everything was defined in yaml, stored in git and was repeatable. A sane user environment meant that we could execute as user and inherit their environment. It has sensible retry logic, and lots of hooks for all your hooking needs. pipelines are useful for chaining jobs together.
We _could_ have written them as normal jobs to be run somewhere in the 36k node farm, but that was more hassle than its worth. Sure its fun, but having to contend with sharing a box that's doing a fluid sim or similar, so we'd have to carve off a section anyway.
However kuberenetes to _just_ run cron is a massive waste. It smacks of shiny new tool syndrome. seriously jenkins is a single day deployment. transplanting the cron jobs is again less than a day (assuming your slaves have got a decent environment.)
So, with the greatest of respect, talking about building a business case is pretty moot when you are effectively wasting what appears to be > two man months on what should be a week long migration. Think gaffer tape, not carbon fibre bonded to aluminium.
If however, the rest of the platform lives on kuberenetes, then I could see the logic, having all your stuff running on one platform is very appealing, especially if you have invested time in translating comprehensive monitoring into business relevant alerts.