In addition to the other comments, I would add that a benefit oil has over water with infusions is the potency of the herb’s properties. Just like how some produce is better consumed raw depending on what sort of health benefits you’re hoping for, some herbs are optimized by longer infusions or gentle heat. Infusing herbs in water without heat I have found decreases shelf life and potency. It also takes longer for water to absorb herbal properties without heat.
I use oil and water infusions but tend to use oils more because they have longer shelf lives and mine tend to be more potent than water infusions.
On the other hand, water infusions are definitely faster, and more soluble/multipurpose. I would use an herbal “tea” as a base for leave-ins, DIY DCs, DIY shampoo, and DIY treatments. It’s very easy to add a little to many things without compromising it much more than how adding water would. It is also a lot easier to overload on oil infusions because they don’t absorb as readily as water ones.
My preference for water or oil infusions on my scalp depends on what I’m trying to accomplish and the schedule of applications. The more frequently I want to use it, the more likely I would choose water infusion, to limit buildup. If the infusion will be washed away shortly after use, like with a preppy, I would go with oil infusion— because the oil would require less prep, have a longer shelf life, and wouldn’t be at risk for buildup.
HTH!