Even with something like First Aid, you can raise it better, faster, when you’re a higher level.
Same with mining. The 30 minutes you spent going around the teen-level zones to get 1 stack of tin and copper ore when you’re level 18, can be done much more easily at level 40 with a mount. Move faster, kill faster, more ore in 30 minutes.
Granted, it’s nice to work up the skill to match the gear you can wear but this is what you would face if you did that. Also you need to know about zones where good numbers or routes exist for ore. Just because you can find that ore in a certain zone, doesn’t mean it’s the best place to get it.
Since you also mention that BS isn’t giving you better gear than you can find or buy (now and then), consider to keep the mining skill up to match the zone but wait on BS. It’s a worthy skill and can be done later also without any penalty to you.
I briefly thought about using my hunter to do BS, but the idea of not really being able to use the BOP recipes makes me think I’d rather work it up on a plate-wearer, even if there are BOEs that can be made. If you think like that too, then without having to create another warrior or pally (who may not prefer that gear over +INT plate gear or weapons), you should keep him on BS.