Most anime don't have high budget. Budget doesn't have anything do to with the quality of the anime. It's about the talent of the animators, and the schedule. The reason why most anime look like shit is that the making is not scheduled properly, and they are not paid properly, so the animators are forced to over-work and churn out mediocrity.
The main reason why an anime adaptation based on a light novel or a manga is announced is because of marketing, to promote the manga or light novel.
Studios like Bones or Kyoto Animation however, adapt things with great passion, giving anime with phenomenal art and animation, and also making changes of their own to suit the visual medium in a better way.