By making the ending not romantic, what point about Eliza is the author trying to make?

The ending is rather romantic in a different kind of way. Social mores were far different, and most people did not marry for love. Shaw is illustrating that in his own eyes practicality wins out over romantic love. We see evidence of this in Eliza's realization that Higgins was destined to remain unmarried. Her feelings for Higgins were certainly romantic, but reality sets in, and Eliza understands that the romance will pass. Thus, we see in the epilogue that she and Freddie live a fulfilled and happy life.