This is the thing I think is a big criticism of almost every art. It's hard to train against what your art is weak in, because it's hard to train against what your partners are not good at. For example, World Taekwondo rules emphasize kicks to the point they're the majority of class. So while a TKD guy might have an idea of how to defend against a haymaker, they're generally not ready for combinations. (This is a generalization, folks).
Now, there are some arts that strike and make it against the rules to grab (Taekwondo, Boxing, Kickboxing) and others that grab and make it against the rules to strike (Judo, BJJ, Wrestling). There's also some arts which try to use grabs to isolate limbs in order to set up their strikes (Muay Thai). I've been trying to figure out how to categorize that third type, and I think "clinching" may be the answer, but I'm not sure.