There is no one definitive answer to this question, as it will depend on the specific website hosting and publishing policies of the website owner. However, in general, most website owners are generally supportive of bloggers posting their personal blog content on their websites.
In fact, many website owners specifically invite bloggers to post their blog content on their websites.
However, there are a few potential caveats that should be considered before posting a blog on a website. First, it is important to be aware of any copyright or trademark infringement issues that could arise from posting blog content on a website without the proper permission.
Second, it is important to be aware of any potential security risks posed by posting blog content on a publicly-accessible website. Finally, it is important to remember that any comments or posts made in connection with a blog post may be visible and accessible to the public, which could lead to defamation or other legal issues.
All things considered, posting a personal blog on a publicly-accessible website generally seems to be generally safe and supported by website owners. However, as with any other online activity, please consult with your web hosting provider or legal counsel for more specific advice before taking any actions.