|choose your specializations wisely...|
Another way I'm thinking is more of weapon familiarity instead of weapon specialization. You could make it simple by saying that a character is at -1 to hit and -1 damage with any weapon they are not familiar with. Tada, they will pick weapons to be familiar with and try to use them. For fighters, they get a pretty good attack bonus progression so it's not the end of the work if they break a sword and have to grab up an axe. They are good at killing with anything. For other classes it becomes a bit more of an issue so the druid may not be as eager to try something new when his pointed stick breaks. I'm not sure what constitutes familiarity but it could be as simple as completing x combats with that weapon or leveling up with it or something. Will this add value to the game? Maybe. I guess I should put this thought back in the roaster to simmer for a bit.