It may not have been as apparent on tour when Eliza just leaves the way she and many others have already done, but there's definitely an "oh no she didn't" in-your-face aspect to Eliza's walking off stage and out the back door in the Broadway version. It's like she took a big red marker and wrote "NO" in huge letters on the side of the house. So I think Higgins's reaction is also somewhat of a "she did not just do that" admiration that you might have for someone who makes a grand gesture when they quit their job, and I think that's reflected in the outsized reaction.
