My own dog was not crate-trained as a pup, although I originally intended to. After this year's Fireworks Night I have vowed to see if I can crate-train him by next year (which may not be easy in an adult dog of a superstitious breed!)Just be careful so being locked up doesn't make things worse.
I actually find it easier to train adult dogs to go in a cage. Did it in 5 minutes once with a 6 year old Mali when I decided I wanted to cage her at a show. Of course it helps if the dog is already well trained and used to learning new things.
Have to say though, I've never used cages for large dogs at home and never will. I do for the little ones but that is only under certain circumstances, mainly at night normally -unless the weather is bad, see below.
As you mentioned above, a wet and muddy dog - which is frequent now I am in a rural area - is so much easier to manage if the dog has a crate to rest in to dry off after walk! The only trouble is, this time of year it's in, out, in, out , all day long. I do this with my toydogs, cage them when they have been outside (doesn't have to have been a walk ,a 5 minute pee break in the garden is enough to get them muddy -furry feet!) and the way things are going, once they're dry again and let out, they ask to go out for another pee, and so we continue all day! Wish I knew what the answer was. I find my little ones want go out every hour at least. The big ones last much longer and them I just lock in the kitchen which is fine -no furniture to jump all over, wipeable surfaces. And only one with hairy paws -the Golden.
What I REALLY want is wellies for dogs that the dogs can put on and take off themselves! :)