@NationBuilder1, I think you are confusing "betrothal" with "engagement". You are describing "engagement" - an intention to marry that can be called off at any point as it is informal - and calling it "betrothal".
In a society that practices betrothal, it is a serious deal. It is when formal agreements are made, money sometimes changes hands, ownership of the woman changes from her father to the husband. And this is why a betrothed woman is treated essentially identically to a married woman when it comes to sex in scripture. She belongs to the husband, any sex with anyone else is adultery, unfaithfulness to the man she is formally pledged to.
In our culture, this is most similar to the wedding ceremony. If a virgin couple have a wedding, say vows and so forth, from that moment on we call them "married" (inaccurately). If she ran off with the best man later that afternoon, we would consider her an adulteress - even though she has not yet slept with her husband. That night, they will consummate the union and become truly married, but we still recognise them as bound together from the time they made a formal agreement to be bound.
That formal agreement is betrothal. The only difference is that in our culture it lasts for a period of a few hours (between the wedding and first sex), while in ancient cultures it could last for years.