The first contact that namecheap made, was just an email that said they will suspend my domain within 24 hours if I do not respond. No matter what content the images had, that is inappropriate business behavior.

The even acknowledged the the site "Yes, we have checked the content of the web-site and based on its not deliberate nature". I have no idea if they really would have suspended within 24 hours, but that is definitely is not how a customer should be treated.

I don't think any important domain should be on such a service, when other equal services will be much less threatening to customers.