"That doesn't have to be there if you don't want it to be. It's been a little while but I'm fairly sure there's nothing specific in Pygmalion or My Fair Lady in the text that suggests specifically romantic feelings."
Strongly disagree.
"I only know when he
Began to dance with me
I could have danced, danced, danced,
All night"
"I've grown accustomed to her face
It almost makes the day begin"
These are some of the most famous romantic moments in musical theatre.
Eliza and Henry's romance in MY FAIR LADY remains merely implicit through much of the libretto.
But it would be a mistake to call it either avoidable or unspecific.
The play is called Pygmalion.
Pygmalion is a mythic sculptor who was not interested in love until he carves a woman out of ivory and falls madly in love with her.
There's a reason the play is called Pygmalion.
Moreover, if anything, Eliza and Henry's romance in the musical is far more realized than it is in the play. Famously, smartly, though somewhat controversially (since Shaw left strict instructions that it be clear that in all future productions of the play it should remain absolutely clear that Eliza does not remain in Henry's life), in My Fair Lady we are blissfully left with the impression that she remains a very important part of his life.
And given that we know how deeply they feel about each other (from the lyrics we hear them share with us, the audience, alone), it is almost inescapable that there attachment post-curtain would be consummately romantic.