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AddType application/x-httpd-php .html
It will have some impact on server performance, since every .html files will have to be parsed. Maybe you can add it just for individual files by using <Files ...> sections.
You will also loose some HTTP headers that the default handler in Apache sets based on the file sent. This is stuff like Last-Modified etc.
So, it should be doable, but it will have a pricetag.