I recently took a look inside of Twig because of this: https://www.phpbb.com/community/viewtopic.php?f=661&t=2567666 

That particular issue is now fixed in Twig 2.x/3.x but other parts of Twig do require at least one of iconv or mbstring to work properly. The version of Twig that ships with phpBB 3.3.1 can't even display the installer but using the yet-unreleased fix, the installer can display the "Check requirements" step properly and only fails during the "Set installation data" step. That's mere happenstance, however, and it's possible that future versions of Twig or the installer will fail before the requirements can even be displayed.

Note that the iconv polyfill requires mbstring for some functions, and vice-versa.