Many data models don't have obvious singular keys. The critical search relationships cannot be reduced to an order relationship on a single column
a priori. Much of the most interesting research in storage models is around increasingly efficient ways of indexing complex information theoretic features across multiple columns in a single structure, with an underlying storage implementation to match.
At some level, every database contains a key-value store. For performance reasons, the hardware always has to be treated this way. Databases work at the level of blocks/pages, but those abstractions are usually hidden from users with a lot of clever logic in the middle that is more opinionated to enable optimization. That doesn't change.
An interesting and important property of search data structures is that, at the limit, a single index that can optimally satisfy all possible queries is equivalent to general AI. It is also completely intractable. Fortunately real-world queries tend to be much more limited in nature. A corollary is that the distinction between indexing, storage, and scheduling in databases is a fiction -- useful for making some things simple but not necessary in any database. In essence, the practice of treating indexing, storage, and scheduling as discrete functions in a database is the opposite extreme. There are a vast number of possible implementations between these two extremes with better properties than either in practical real-world databases.
As a general design principle for scalability and performance reasons, you want to organize your data model around a single indexing mechanic. Consequently, it is critical to maximize the expressiveness and efficiency of any particular indexing mechanic. At the limit, with a good algorithm, it is equivalent to having an index for each column, with the ability to efficiently search more features of the data and without the overhead of actually having an index for each column.
I think we are entering a new golden age of database technology where the boundaries between elements we treated as discrete are much fuzzier.