There has been an MQTT module for Prosody for ~5 years: https://modules.prosody.im/mod_pubsub_mqtt.html

I'm not aware of anyone using it in production, or asking to - so it's not received a lot of attention. For my own projects I've tended to prefer bridging to XMPP in other ways, but it was fun to work on.

I found a number of things surprising in MQTT, for example the lack of errors in response to commands (such as publishing), with the only solution to be just closing the connection entirely.