I've read some analyses of this film interpreting it as an exploration of masculinity. Zaroff's and Rainsford's thirst for hunting is an extension of the testosterone-charged need to conquer one's target. Including in the story Eve as a sort of prize for whoever wins the game, then, adds an extra layer to the commentary of the dangers of not tempering one's masculinity. Rainsford's attraction to Eve was no doubt more benevolent than Zaroff's who was ruled by his appetites. Rainsford is able to win the game and Eve because he has control over his masculinity.
So, yeah. That's one possible reason why.
Half-Blood 15
God give me courage to show you, you are not alone ~ Phantom of the Opera

I appreciated the inclusion of an attractive woman in what otherwise would have been a sausagefest.

Why? Because man boobs aren't attractive.
..Joe

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And Fay had one of the best screams in movie history!

IndeedFay Wray sold movies, she always made them worth watching because she could always play quite a character in any one of them.

Oh yeah. And why have monsters, psychopaths, brain-sucking aliens or Indians for that matter? They merely make the movie interesting.

Amen, and case closed.

I'll be honest while I could have enjoyed the movie without the girlshe sure was something nice to look at.

Reminds one of a Sullivan's Travels quote from 1941 as well.
"There's
always
a girl in the picture. Haven't you ever been to the movies?"
'We're not in Medford now. We're in a hurry.'

"Because the public - bless 'em - must have a pretty face to look at."
~ Carl Denham (King Kong 1933)
I found it a rather appropriet quote since the two films were shot simultaneously by RKO and it answers the question as to why stories like The Lost World, King Solomon's Mines, Most Dangerous Game, and The Island of Doctor Moreau have a female character added to them when they make it into a film.
"Attempted murder? Now honestly, what is that? Do they give a Nobel Prize for attempted chemistry?"