Looking at the wear that you experienced after such a short duration is a pretty good indication of why they're not widely used. I'd felt-wrap it before subsequent uses to reduce the surface-wear.
I was going to tell you to soak the cork before use, and expound on the benefits of cork soaking, but I haven't soaked cork since a mixup in 68' where a buddy and I accidentally soaked each other's corks.. Or was it 70'? Might as well split the difference...
I got into beater experimentation after seeing You Tuber rdavidr make a bunch of weird ones.
If nothing else, he got my creative brain going.
I've taken an old felt beater and trimmed it down to the size of a golf ball core. Then I'll take a cork ball from a craft store, hollow it out to fit and glued the beater inside. Now I have a cork-wrapped beater with a solid core.
It's good for lower volume gigs where you want a bit more punch. The cork will get a flat spot over time, so each time you use it, tweak the beater a bit.
Cork alone will come apart over time (usually from the inside first), so I'd recommend something solid inside.