A couple of reasons:

First of all what one wants in terms of faucet designs is very personal. As such there are many many models to choose from. This makes each model in be produced in relatively low quantities, and be more expensive. If everyone would use the exact same faucet, they would be basically free. And you do see some models being used in new construction that are very cheap indeed, just because of the higher volumes.

Second of all, the tolerances and finishing involved. It's relatively easy to make a faucet that works, the designs have been perfected long ago and modern manufacturing can easily produce a working model. However to create a faucet that feels nice, that doesn't make weird noises, opens and closes smoothly etc. is a lot harder. I've had cheap faucets before, one of those single handle deals. It would take more force that I would like to open the tap, at which point it shoots open so water sprays out. The range in temperature is insanely hot to insanely cold with only a tiny single spot of normal temperature in between.

Third reason is they are made from a lot of parts and with materials that need to be handled really delicately. Chrome finishes that scratch easily when handled in properly, leading to the whole thing becoming instant scrap. This leads to hand assembly being the only option. And often it involves a lot of small parts that need to be placed just so. This adds a lot of cost.

Fourth reason is the materials themselves, often quite expensive to start with. Large parts being machined out of a single piece. By definition everything needs to be corrosion resistant. And it's one of the products where we still expect them to last 15-20 years easily. Not like the consumerism that's forced a 5 year lifespan to be called long in the modern world. The finishing coatings are often chemically applied with expensive materials and taking a long time. And a fully polished finish also takes time and is often done by hand and takes some skill.

Fifth reason is brand names. Just like with any designer thing, brand names and designers are a large part of the costs. You can often find designer faucets for outrageous prices and cheap knock offs that can be trash or sometimes even better than the original for half the price.