A coat will not be too much bother too hand in for dry cleaning. My experience with wool/polyester blends is they can even come out nicer after a wash than from dry cleaning. I have an old duffle coat, and when it was new I handed it in for dry cleaning. It's wool, with a percentage of polyester and just a bit of cashmere. It was a few years old the first time I washed it, and it had been in for dry cleaning several times, but since it was no longer brand new I took the chance.
I had it in the washing machine on 40 degrees, I had an extra rinse cycle after spinning, took it out, shook it up, stretched the seams, and I swear the wool fluffed up almost like new. It looked much better than the last times it came from the cleaners.The steaming done at the cleaners flattens the fabric, and in this case it wasn't to an advantage. I know some steam coats like these on a hanger with something that look like a vaccume nossle. I don't think I would ever dare do it with the genuine heavier duffle or some types of pure wool fabrics.
When it comes to garments like jackets and coats I think it's all about what the fabric can handle and some times dry cleaning isn't to an advantage. Wool fibers in general are fine with both types of cleaning when done right.
If the coat is all in one color, there is no problem with dyes bleeding. After washing or dry cleaning there is often a slight change in the fabric, but it's just that it's no longer brand new.
Wool can be boiled, when test square of washable pure new wool are put in a pot of boiling water, left there for about 10 minutes, picked up again, it will look just as good as the square that's never been washed. I have seen this test done on knitted wool as well as woven.