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I implemented something like this! The Dr. Lojekyll [1] datalog system was built around the idea of inputs as receiving messages over time, and publishing outputs (also as messages) or responding to queries (using materialized views). It worked quite well, but it's differential nature ended up being the downfall for the usecase we had in mind.

Specifically, it had no way to "extend" its consistency model out to consumers of its messages, and so if consumers were also producers, then this distributed system as a whole could enter into a state where parts of it are lying to itself!

Otherwise, there were some really fun things you could do with it. For example, we could have per-client databases that would bring themselves up-to-date given the differential outputs of the server database. This would let you engage in a kind of manual sharding of data.

[1] https://www.petergoodman.me/docs/dr-lojekyll.pdf