It seems that phpbb\textreparser reparses text which is already parsed in correct format.
Or, probably, it reparses not everything but newly added objects (like new posts etc).
Via the cron job phpbb\cron\task\text_reparser.
That were found while developing the MediaEmbed extension, the scenario is:
disable mediaembed extension
post youtube video URL
enable mediaembed extension
force reparser cron to run
reload the viewtopic page with the post (several times probably)
The issue (with reparsing user post signatures): https://github.com/phpbb-extensions/mediaembed/issues/11