Straightforward, Witty
Though Henry Higgins claims to be a regular John Milton, Shaw doesn't let him get too poetic. He has too many important topics to tackle, and he can't be bothered with heavy symbolism, complicated metaphors, and big words.
Above all, Shaw wants his characters to speak, whether with Eliza's almost incomprehensible accent, Doolittle's strange charm, or Higgins's cynical reason; he wants us to understand the variety of ways English can be spoken.
And so we get Higgins imitating Eliza—"Cheer ap, Keptin; n' haw ya flahr orf a pore gel"—and what Higgins calls Doolittle's "native woodnotes wild." Each is distinct on a grammatical level, and, when performed, is delivered with a different accent.
Remember how at the beginning Higgins is able to tell the people where they come from? Well, even if we, the audience can't pick out the different accents, it's the director's job to sort that out. Tough, huh?
It's a good thing Shaw also has no problem with telling us what characters are like right off the bat. He lets us know from the very beginning that Higgins is a bit of a baby—it's in his character description—and we get plenty of confirmation later on.