This is pointless semantics, like the perpetual insistence on correcting "monopoly" to "oligopsony" or whenever monopoly is discussed.
No one knows the word "dower," and the term "dowry" is used pretty widely to describe the entire mess of different customs that do and did exist. IRL, these are all symbolically complex and play a role that is usually different to the symbolic one.
Engagement rings are a riff on these.
It is not hard to understand why dowries are a thing of the past in western society. But it is still a thing in other parts of the world.