Can a character with the Magic Initiate feat use the appropriate arcane/druidic/holy focus?

The Magic Initiate feat lets you pick a few spells from a number of classes’ spell lists, each of which has their own rules for using a focus in place of material components – notably, it excludes the one casting class that cannot use a focus of any kind, the Ranger.

Also notably, while the feat makes it explicit that you use the appropriate attribute to cast that class’ spells – but not that you gain the use of the appropriate focus. Is there a reason to believe you also gain the ability to use the focus, as per the appropriate class’ Spellcasting (or Pact Magic) feature?