That would be great!
There was some investigation into using log aggregation tools like Splunk in the Mendix cloud at some point recently. If you happen to have Splunk, you might reach out to Mendix Support and see if they can do anything for you.
Have a look at the logging module in the appstore:
This logs everything in Mendix objects, but should give you a starting point to log centrally.
Well, not to my knowledge. My third-party answer would using the ELK-stack. My mendix answer would be to add a Mendix App to your landscape that takes care of the logging-functionalities. This log-app will publish services allowing consuming apps to send their log-messages to the log-app.
In the consuming apps you will probably be using app/159 mentioned by Erwin, which you will have to extend somehow with a function to call the log-app to send the log-files over there. And yes, you will have to add this to every 15 of your apps, but it will be small and identical everywhere. Not much harm there.
This will also help setting it up: https://ww2.mendix.com/cw-integrating-microservices?utm_campaign=esw035&utm_content=DevSite, if you are not yet already familiar with it.
Like Cillus, I am interested too in a working version of your question. Tons of use cases for this. If you would set this up as a separate Appstore app set up the basics and invite people like Cillus and me to help out.