Not true. For example, a compiler can be a pure function. It accepts input that is the source code, and outputs the machine code. There's no side effect there. I admit it needs minor scaffolding to always read all of stdin first, and write all to stdout at the end, but the programme, as written by the programmer, is a pure function.

This is one of several ways that Haskell worked before there was an IO monad [1], all allowing pure functional useful programmes.

[1] S. Peyton Jones. Tackling the awkward squad: monadic input/output, concurrency, exceptions, and foreign-language calls in haskell. Technical report, Microsoft Research, Cambridge, 2010.