First, she can’t climb over or pull the gate down now, but she might be able to do so in the very near future. (Think ahead to how you will handle this problem in the future if it persists – do you want to put a lock on her door?)
Second, if she establishes a habit of falling asleep at the gate, she’ll have that association and you’ll have to work with her to break it eventually or deal with it for as long as it may last. (Better to deal with it now than later when you have another baby on the scene.)
Third, she’s close to potty training age and while she is probably wearing a diaper to bed now, eventually she’ll be in underwear and may wet the bed. It’s way easier to protect a mattress than an entire floor area (though disposable training pants could solve that issue).
Lastly is the message that it sends. If you tell her with your words that she has to go to bed and that her bed is for sleeping but you tell her with your actions that it’s fine as long as she’s in her room and not making a scene, then she’s getting a mixed message.