When looking through the budget sarashi tag, I see that there are quite a handful of posts that show the sarashi being mostly worn loosely/untied (ie. post #4777159, post #3438640, post #3067568), or still covers the breasts fairly well (ie. post #4561760, post #4692677, post #4288942, post #3372709, etc.).
Looking at the initial wiki for the budget sarashi tag (before I revised it for clarity) it says:
"Based on sarashi but when the girl/character does not have enough binding tape to actually bind anything."
The wiki seems fairly vague, though I thought that budget sarashi is typically reserved for sarashis that look like very narrow bands of cloth that barely covers the chest (ie. post #3958847, post #4799157, post #4742779, post #4495654, Kantai Collection's Musashi, etc.).
Conversely, I don't think the budget sarashi tag applies if the sarashi could honestly pass off as a regular tube top that reasonably covers the breasts (ie. post #4561760, post #4692677, post #4288942, post #3372709, etc.).
Thought I may hear opinions before doing some tag gardening.
Updated