What licenses the omission of an article in a countable or singular noun phrase?

It may not be possible to define a rule here. What matters is what is idiomatic.

In English, to be sent to market means to be offered for sale on the market. This is an abstract concept. The market has no physical location. This may occur in multiple places. "Around 85% of ducklings would survive this eight-week rearing process to be sent to market."

to be sent to the market is used in contexts like "My mother sent me to the market to buy eggs." This means being sent to buy eggs at the market. This is a physical location. There is a particular marketplace in mind.

This is also used in economics in circumstances like: "What signal is sent to the market when a firm decides to issue new stock to raise capital?" This is saying the something is being communicated to an area of the economy (4d: MW.com: the area of economic activity in which buyers and sellers come together and the forces of supply and demand affect prices). Note: this does not mean that something is being offered for sale on the market.

There is no hard-and-fast rule for how to determine when the article is used in English, and the rules even vary within different varieties of English: The Brits can say "sent to hospital" while North Americans have to say "sent to the hospital." But we both say "sent to school" meaning that the person is enrolled for education at an academic institution. (While being sent to the school means being sent to the physical location of the school building.)