I don't think that's a problem. What turns logs into a problem is misplaced expectations on what is their purpose and how you should use them.
Logs are collected with the express purpose of being ignored, and as a safeguard in case in the future you need to check an audit trail of what you were doing. After a while, once the odds of those logs providing any value drops enough, you can safely delete them.
Your tool is only as good as you make it out to be.