There wasn't really anything wrong with the king's argument here. It eats into a significant portion of their budget on the project, but the alternative in this setting is trying to buy it while it's on auction. Such a valuable item on auction is probably going to rapidly shoot past it's estimated value via the bids. By trying to purchase it directly now at that estimated value, they're honestly getting a discount if anything.
The way the king is handling it also shows he knows what he's doing in how he's handling the other asset from this situation: the main character. He surely doesn't want to blatantly attempt to fleece the person who was capable of handling that situation, so this is also an investment in a favorable relationship with a powerful ally. The baptism, the medal, the title, and the purchase of the materials are probably all calculated moves to some degree in favor of this end. In particular, the title and that baptism grant the king and the church some small amount of control over him as one of their own already.