Yeah, half is okay. You don't even have to replace it fully, though doing so keeps the starter hydration stable, which means it'll slot into recipes more precisely. Going by halves makes the math easy.
Discard is starter, it just isn't at peak. So it won't give the best results for bread, where you want the culture at its most active and energetic. It'll still work for sure, and it won't even be bad bread. To the contrary, it can end up being damn good. It just won't have as open a crumb usually, unless you do longer ferments, or at least that's been my experience.
All a starter is, is a culture of yeast and microbes. When you feed the culture, everything has fresh, abundant nutrients, and the waste material is diluted. So, the half that you keep has the ability to grow rapidly, with the microbes reproducing at a higher rate, as well as producing waste at a higher rate. That means more CO2 and alcohol.
As those fresh nutrients get used up, the wastes accumulate and the microbes slow back down their reproduction. That's exactly the same thing as happens when you're making bread, it's just that when you're making bread, there's so much food for them that they don't slow back down their reproduction (and the CO 2 production with it) until well after you'll be baking it.
So, when we discard, what is being discarded is a deeply flavored mix, with some tired but perfectly viable microbes. If you put them into the usual recipes for discard and let them sit longer, you've essentially got a new batch of starter. But discard recipes don't rely on the CO 2 production for loft, and they do rely on those waste materials for their sour taste. Those wastes are at their most concentrated before feeding on an active schedule.
That's essentially the goal of long, cold ferments. You get the microbes reproducing and producing CO2 fast enough to rise, but slow enough that the waste materials accumulate for a deeper flavor.
That's why cool stored starter is so intensely flavored. The waste climbs to its peak right where it's going to start killing off the culture by the time you feed it weekly (or so). The yeast and lactobacilli are doing their work slower, but for longer. Less bubbles, more tang.