So what's the purpose of using 10, 12 and even 14' foot poles when crappie fishing?

So you can reach spots and jig vertically. Nobody told me that, but it is what I assume and why I use them.

Anything longer than 12 is generally used for trolling in shallow water to avoid spooking fish. I've heard of people going 16 foot+ at times. Get the bait further away from the boat and trolling motor/electronic noise.

Gives you a stealthier approach for certain types of fishing techniques.

Spider rigging getting them away from the boat

Actually I like using my 10 ft. poles right now while fishing the shallows for spawners. It's real easy to pitch your jig a long ways with a quiet presentation. Needless to say they're not worth a flip under a bridge.

Great for fishing timber. You cath the fish before your trolling motor has a chance to blow them off the tree.

I use them at the slip. If a guys catching two slips down I don't even have to get up to drop my jog in that hole just kidding! All of the above answers make sense to me.

You want to stay as far away from a crappie bed or pile as you can to keep from spooking them. The longer rods give you the ability to stay farther away to not scare them. The same goes for trolling. The long rods keep the baits from the boat so the motor or sound of boat does not scare them away from a spot you want to fish.

What kind of reels and line do you usually use on these poles?

Either bait caster or spinning reel. Which ever you feel the most comfortable with. Line is also personal preference; 8-10 lb test is sufficient for most applications. Some prefer braid, some mono. There are plenty of threads on here discussing the pros/cons of each.
Ten foot plus poles are not intended for casting, although you can cast a jig easily with a spinning reel. Long poles are intended for vertical jigging, trolling/spider rigging. Especially helpful in spring for shallow fish whether you're on the bank or boat. I can keep the boat away from fish in shallow water so the trolling motor or other noise doesn't spook them. And I can reach more places without having to re-position the boat so many times.

Another reason is when you are fishing with someone in their boat and they are staying on the brush pile at the front of the boat and there is NOT enough room for your to fish over the pile. Then, you pull out your 12 footer and relax in your own seat - and still fish the brush pile like the person operating the trolling motor! And if you are lucky - catch more crappie than the boat operator!!

There's several for me. First is when the fish are spooky u can get the jig in there before they notice the boat or b4 the boat bumps into timber on windy days. 2nd u can cover way more ground vertical fishing around stumps.
But for me, the #1 reason i use a 12 ft jig pole is because of the fight. A big crappie will give u a great fight on a limber jig pole and it may take a full minute or sometimes two to land her. I fish with a guy with a 6ft bass rod and he just hammers the fish str8 to the boat.
I enjoy fighting the fish and if she wins so be it.

So why are only the crappie rods that long? And not others like white bass?