So in other words, the application will work just fine the day you sign off assuming the client doesn't update the language core.

Which is no different than with Dreamhost in this scenario. If, for example, PHP 5.X or 6.X ends up breaking your code, it's not like Dreamhost is going to debug it.

There's no functional difference here between PHP and any other language except that the hosting provider will automatically update PHP. And there's no guarantee that won't bork something else (which they will also not support).