I can certainly see some of the advantages, but what might the disadvantages be?
Pages that contain no PHP code would be parsed for PHP code. A negligible disadvantage is the overall scheme of things.
Besides, URIs and file paths are not the same thing, so in the end you would map the actual file path, be it with a .html or .php file extension, to the actual URI, which does not even need a name suffix.
The big disadvantage for me is that I don't have PHP or MySql on my work computer.
Install a webserver, PHP and MySQL on your computer.