You can already cleanup logs faster with a timer in forge component DBcleanerOnSteriods, and you can already disable logging on module level. Not having logging at all doesn't make sense to me in an enterprise organization. Most companies actually complain about not enough logging or to limited log retention. Maybe you should focus on the root cause of too much logging and fix those.

Ignoring the problem would be like sweeping dust under the rug. The most important thing is to identify the root cause of errors and fix them. A productive environment where issues go unnoticed poses a significant risk to the company's operations. 

You can disable logging for each module in Service Center. Perhaps disabling this on some of the "heavy-offender" applications/modules that keep filling your logs would prevent the other issues you are experiencing on your platform. Although, if you have apps logging this info that much, it is better to resolve the root cause rather than ignore it, but that is your call. I'm not sure what version you are on (O11, or ODC). I am on O11. If you look the module up in Service Center and look at the Operation tab you can enable/disable Activity Logging: