Besides, plasticizer migration works the opposite of how you think: it migrates from soft plastics to hard ones and softens the hard ones. Plasticizer migration would result in the plastic going soft, not in the rubber going gooey.
Yup. The worst offenders (as in way too much plasticizer) in my experience are fake "silicone" leads, which are really just overly-plasticized
PVA PVC.
The result is that if you keep them in a plastic box, the lead can literally meld into the box, due to the plasticizers.
I often want softer multi-strand wires, and don't usually need the high temperature capability of silicone leads, so I wouldn't mind them being
PVA PVC or some other non-silicone plastic, but the migrating plasticizer makes them annoying to store; they need to be stored away from anything plastic, including cutting mats and such.
The issues with plastic additives have existed for as long as plastics have been industrially manufactured.
Back in the previous century, when reversal/slide films were still widely used (called "dia" or "diafilm" here), sometimes the pocket sheaths used to store them in books had additives that caused film destruction in a few years to a couple of decades.
For soft overmoldings, I do believe butyl rubbers are the worst offenders, as they become sticky (especially so from human skin oils) in a few years. Some varieties become stinky (vomit smell), as they slowly decay, one of the byproducts being butyric acid.
AvE has mentioned these butyl rubber overmoldings in his BOLTR videos on Youtube, including how oils speed up the decay of the overmolding; so that for industrial tools and tools used with oily hands (think mechanical repairs), they really don't last long. My own worst experience has been with bicycle handles, which became tacky, more tacky than 3M post-it notes, in a few years, with that recognizable butyric acid vomit smell. Eww. Oh, and hand cart wheels, which were some black plastic with plasticizers, that stained a plastic/vinyl floor mat with yellow blotches when they sat there for a couple of months. Dammit; should have waxed the mat better.