In case my comment above isn't clear, the entire notion of this is absurd. When you configure apache, or set .htaccess, you are simply telling apache what to do with various extensions. The notion that there is any overhead on a php page, for example, with .html extension, is incorrect. And why would you add php processing to pages without php? The extension is just some letters after the dot. You can have a straight html .php page, or a pure php .html page, makes no difference, and if it somehow does to that hoster, that's a very bad hoster, which will almost certainly make you suffer in many ways.
Since this is something you can set in your .htaccess, or in apache configs, you do it, presumably, because you are planning to use php on the pages, which means, there is as far as I know zero difference or overhead increase if the extension is .html over .php, in both cases, apache hands the processing to php, which then does its thing, and returns the processed page html output to apache, more or less.
I too started with low end cheap hosters, wasted untold hundreds of hours of my life, which I will never get back, working with bad cheap hosters, and now won't do it, there's no reason to, all it costs you is time, a lot of it.
If your time is worth more than about $2 an hour, you will never gain anything or save a cent using low end, or middle grade, hosters. And if your time is worth more than 10 bucks an hour, you will never save a cent using anything but high end hosters, shared or otherwise.
And if your time is worth actual professional salary, then you are making a serious mistake. One I've made many times, or rather, allowed clients to make, but now will not do anymore. I find a few fully invoiced low end hoster failure support instances easily convinces anyone that the cost saving was purely an illusion. Or the site going down the first time any site on the box gets any load, whatever.
"Forbidden in the TOS/AUS of a large number of shared hosting sites is the phrase "Force html to handle server-side code (like php and shtml) to help reduce usage." as a prohibition."
I'd like to offer a suggestion: I have NEVER seen this prohibition on any even mediocre hosting company. Never. Not one single time. So I would take that and add it to the list of "how to identify bad hosting companies". Even bad hosting companies have not done that in my experience, so this must be some seriously low end stuff, but I will resist the urge to get into specifics, except to note I'm not surprised to see the name hostgator mentioned in this context.