My router stays online 24/7. It already has a web server built in. I could hack it to make it serve a public website.
But there’s absolutely no way I’m going to do that. The security and maintenance requirements are just too much of a PITA.
It’s much easier, more secure and more reliable (and likely cheaper once you figure in depreciation and opportunity costs) to set up and maintain an instance in the cloud, or a serverless site.
And if you don’t like the big cloud providers, there are many smaller outfits that can do the basics - compute and object storage are all you really need for a small site.
Consumer hardware and software are not really well suited to running publicly faceing websites.