As far as I’m concerned the primary reason to include Radagast in the movies was to canonically establish that all the Wizards of Middle Earth were into drugs.
Saruman chided Gandalf for smoking so much weed and noted that Radagast had fried his brain doing psychedelic mushrooms, but you don’t get a nickname like “Saruman the White” unless you’re doing a lot of cocaine.
As for the unseen “Blue Wizards,” I’m picturing something akin to Walt and Jesse working away in a meth lab somewhere.