Also initially read - lazydog as name, it would be cool name as well :)
I see it being useful for doing quick testing or hackathons, when setting up some infrastructure is not worth it the hassle or time.
Would suggest adding PayPal donate button for free tear users.
As an additional feature would suggest adding export of logs as archive or export/import to some other log aggregators.
Do I really want to POST logs? What if the logging endpoint is not available? Don't I want log delivery uncoupled from the application, so logging failures don't become application failures?
How does this comply with privacy laws/requirements (e.g. GDPR)? Storing PII is a liability and you expose yourself to legal risks.
Edit: Just to clarify: it's not an aggressive question, I'm mostly curious what is your strategy about this.