If they're static files, then by all means, use file_get_contents(). But if they're PHP scripts then obviously include() is called for.
In anycase, including dynamic template like this is a bad idea in general.
That's a very broad statement. I wouldn't say that in general. It depends on the use case.
This is a common technique in implementing a templated site by new PHP developers and will likely bite you in the butt eventually.
It will likely burn you? I wouldn't say that either.
My biggest worry, is that those included files are not properly protected via file permissions, and someone on your shared server adds some sneaky code.
That's a legitimate concern in general, and something the OP would be wise to consider, but what leads you to believe that those files in particular are likely to have permission problems? If the script that pulls them in [using include() or file_get_contents()] had a permission problem, then that script could be compromised itself.
Or worse, someone finds a whole in your code somewhere else and over writes one of the included files whitelisted as "safe".
The problem there would be the permissions on those files and the insecure script that allowed them to be overwritten, not the legitimate use of include() (assuming it is legitimate).