agreed. For example C is considered general purpose despite not being Turing complete.
Actually, C fails the general purpose language criterion too, because it's simply not a good choice for many different and common uses. It's a good choice for very specific uses at this point.
C treats computer memory as an array of bytes indexed by a pointer type that can take only finitely many values. If the pointer type can be cast losslessly to `long int` - which is usually understood to be 64 bit - then this byte array has precisely 2^64 entries. That implies that C programs have an absolute limit on the amount of memory they can use (2^64 bytes). That's obviously true, because each call to `malloc` fills up another entry of this finite byte array. C therefore can't simulate a Turing Machine, because a Turing Machine can use an unbounded amount of memory.
If you use a file system, or another source of external memory or storage, then the above argument no longer applies.
So I'd argue C-as-specification (not as existing implementation, I don't know) is _theoretically_ Turing complete. Yes I agree it's a troll.
If we use "useful" definition of being Turing-Complete, then even `printf()` alone is already TC.