I think it may vary from headphone manufacturer to manufacturer, my SA5000 pads have done the opposite of what you've described - fresh out of the box they were stiff like new shoes or a new wallet, but after a lot of usage they've "broken in" and are very soft and comfortable. My K1000 has done the same thing, but I'm not so sure those are real leather. I think climate may also play into this, but I live in a fairly dry region (I think it's about 8% ambient humidity today) so unless you're in a dehydrator I don't see it being a problem (I know rot can be helped along by extreme humidity though).
Some other bits to add:
I know that leather, like other hide products, benefits from being handled by humans (or probably very likely other animals) because oils are returned to it, but I'm sure this can be overdone.
I know that leather can be "sealed" and that will ruin it (this is based on outdoor/mountaineering equipment made from genuine leather, basically the material has to be able to "breathe" to some extent).
I know that eventually it will rot into a cakey and horrible thing that is the stuff of nightmares (this is on the order of decades though, not months - I've only ever seen this on book bindings).
The saddle-soap products are probably a good place to start, I've seen them used with great success on all sorts of leather work (including shoes, gloves, boots, jackets, etc). Alternately, look at the treatment products for garments (like what you've mentioned for the purse). If in doubt, I would probably contact Beyerdynamic and ask what their suggestion is for caring for the pads (perhaps they even sell a treatment product?). One thing I would be (personally) worried about is leaving a very greasy/oily layer on the pad that will transfer to everything it touches, like a polish/wax (I'm just seeing it leaving black rings on your head).