Letting wine reduce before braising I've seen recipes for braising (sorry no sources available) that instruct you to deglaze with wine then let it reduce by about half. After the wine has reduced, the next steps are to add in stock, more wine and aromatics, let it come to a simmer on the stove then pop it in the oven to braise.

I'm curious why let the wine you deglaze with reduce if you are going to be adding more wine in before putting it in the oven? This makes no sense to me.
Just a question of flavor layers.

Reducing the wine after deglazing will create some deeper flavoring.

It will remove some of the wine's acidity and concentrate the flavor that will complement the stock and wine that will be added later on in the recipe.