Routing is all about manipulating operations at the shard level, not index level. You can only add a document to a single shard within an index.
You can search multiple shards of course, which is why multiple routing values are permitted there. From the docs:
Routing
It is possible to associate routing values with aliases. This feature can be used together with filtering aliases in order to avoid unnecessary shard operations.
It’s also possible to specify different routing values for searching and indexing operations:
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