If the girl has to be the one to ask for exclusivity, is the relationship more likely to be doomed than successful?

I've never been in a relationship, but I always felt like the guy should be the one to initiate this conversation rather than the girl, since the question is essentially an ultimatum. So if the girl asks the guy to be exclusive, he can't say no or ask to wait because she would just leave (or sense the hesitation and commitment issues from a guy who wants to "wait", then leave) and so he has to say yes so he doesn't lose her, even if their desire for exclusivity isn't aligned.

Am I wrong to think this?

If the girl has to be the one to ask for exclusivity, is the relationship more likely to be doomed than successful?
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