The fashion for brass ( usually) drawer pulls might not have had much to do with the cost.

For the more modest households, there's the general lack of drawers, or things with drawers, until you get into the 16th c. Instead, there are a lot of chests. Those have lids, of course, and not pulls like drawers. But those also often came with locks. And cupboards, and linen closets, etc. had locks as well. Things were expensive, so things were locked, and the mistress of the house could be heard from a distance, as she had a large bunch of keys jangling authoritatively at her waist. The pull, for cupboards, was usually the key. Chests also came in different levels of security, with simple coffers that just had a simple lock to strong boxes bound with iron with interior cross bolts to make them nearly impossible to pry open.

However, chest with drawers and little dangling pulls on them seem to become rather popular in the 17th c. , like on this Spanish desk and this Spanish table. Before that, I am not very certain, but if there were drawers they were often rather hidden, like on this French 16th c. piece But that's not a matter of not wanting to spend money on metal pulls- obviously, someone spent a very, very long time doing the carving on this. Likewise, on this 17th c American sideboard ( an amazingly rare piece) you can also see wood knobs but a great deal of turning and joinery. And, on this Spanish desk, even though the lid has pulls, the drawers have wood knobs. So, really, it does not seem to have been as much a matter of economy as much as fashion.