First to the root thing...
I'm not sure how a "chicken foot" is an improvement. I don't think you should do anything in a hurry... for one thing this is a not level - not straight photo... so how it really lays could be much different. I'd give it several years and see if any of them start to fuse so you can maybe carve out parts but not all. Azalea as with so many things can fuse roots together and become bumpy interesting things... a chicken foot... *yawn*
So think twice. Don't think about the "now" think about 10-20 years from now.
As to the azalea in question... there's too much congestion in the area where all the branching erupts from the trunk. It is in effect a whorl of branches. It needs to be selectively pruned back to only a few branches very soon or the reverse taper that is already becoming evident will get much worse. While this will make the tree somewhat unattractive for some time, it'll serve the long term image of the tree in the end. Without being able to look at the tree from all around and the interior, it would be very difficult to tell you what I'd remove... if you bought it from a bonsai nursery, they should be able to help you select the right things to remove.
If you decide to repot the tree now, be sure to remove any flower buds that are coming in at the same time. Don't let it bloom. The best time to repot them is actually a bit past... and any time you repot them you should not let them flower. I know there are a lot of theories that it should be done after flower, but things vary depending on the state of the tree... so while I believe you could still repot it without danger, I wouldn't likely do hard root work, and I would make sure no flower buds were present.
But you could do a moderate cleaning and pruning of the roots and put fresh soil in it. Always be conservative with root work until you feel very confident about it. That usually takes a few repots with the same tree.
Hope this helps...