scaling down batch size

Can you simply halve the ingredients if you want to make a 5gallon batch but the recipe is for a 10gallon batch?

Yes you can.

I assume that goes for the hops too?  I guess the wort concentration would be the same, so halving the hops would work equally well?  This leads to the question then: why are recipes always size specific? why not just say “pounds/gallon?”

Tradition I would guess.

I prefer to think of recipes as OG and percent for grain bill and IBU and oz/gallon for hops. This is kind of a universal way to describe a recipe. Its also an easy way to “think out” ideas in your head. From there it’s the same math exercise no matter what batch size you’re using.

^^^^^    Yup.  That’s why I like seeing good recipes with grist %, OG and IBUs.  Actual amounts are specific to batch size and efficiency.

Most recipes are designed for a particular batch size and when writing a recipe convenience tends to play a role in the ingredient volumes used. You are likely to find full pounds or ounces used in recipes rather than 2.3443 ounces. It’s easier to buy and measure in convenient increments. People can scale recipes as they need it.

At homebrew levels you can generally scale from one size to another without problems but when you are jumping from a five gallon batch to a 15 BBL commercial recipe the mechanics of brewing at that volume changes sufficiently that a linear scaling does not always work perfectly.

+1 to that, noticed pretty quickly that extract was often called out in multiples of 3.3 for reasons of convenience.
As far as recipe scaling goes I have noticed that in Beersmith even going from 5 to ten gallons with out checking the adjust for bitterness and color box (which then yields a linear ramp up of ingredients to vol) that the IBU’s will vary slightly. If the IBU’s can change with size than I would imagine so can the usage of late hop additions though we don currently have a way to quantify these additions at the homebrew level as far as I know. We just smell and taste the affect on the beer afterward. Recipe size for home brewers may not be crucial, or even necessary but it seems to me that it helps to maintain accuracy and gives inexperienced brewers the best shot at nailing a recipe first swing and without math or software.