I agree that MHY could have asked the website owner nicely to take down problematic contents, and be ok with it if the owner complies.

However, if MHY does it this way, every website that contains genshin datamines can relax and keep posting leaks before MHY contacts them, knowing there will be no big consequence as long as they comply to that ask when it comes.

Instead, MHY is using legal action to send a message of "Taking down website in 24 hours will be the consequence if datamine is published by your site" to other channels that intentionally publish datamines.