What would this accomplish that self hosting synapse doesn't?
It's totally possible to self host the official matrix 'synapse' daemon for self hosted slack-like functionality within an organization, and use the official 'element' client or any other compliant matrix protocol client. If it's for something like company slack-like functionality you can choose to federate or not federate.
https://github.com/matrix-org/synapse
I have one setup where the synapse daemon lives on a VM that's only accessible in company internal RFC1918 IP space so you can only connect to it if your laptop or other device is also on a split tunnel VPN.
Of course you could run it with a public IP as well.