The other way around. If I'm not storing my messages today it's probably because it is too expensive in terms of storage or compute to do so. But, presumably, you can't do that any cheaper than I can. And now we are duplicating the work so even more resources are being consumed making it that much more expensive than just doing it myself.
It seems like your service is something I'd want to run pointed towards my Kafka/RabbitMQ/whatever servers. I don't see how duplicating that stream is cost effective.