I think with the current origin companions, some of their classes are too intrinsically tied to their story.
Wyll, Shadowheart, and Gale's stories are deeply class driven. I'd say Lae'zel and Astarion have some flexibility, but it would still be too immersion breaking from a D&D standard to implement the Divinity class switching system. It simply doesn't fit the tone of BG3 (considering your companions are mostly reluctant allies at first, it'll be quite jarring for them to be open to letting you choosing their career)
I think the issue is less that characters are locked into classes, and more that the combination of not all of the classes AND companions being implemented yet making this game feel more limited than it actually would be.
For example, I have zero interest in making a Druid character myself, but I would most definitely have wanted a Druid companion in my active party. I think this patch really should have had the Druid companion to go along with it.
I hope if the next update adds in a new class, their associated companion (or the Druid or Ranger companion) gets added in too.
Considering all the work (voice, dialogue, and reactivity) that Larian is putting into each companion, we probably won't see every class represented by a companion. Mercenaries (player made companions) is most likely what we'll need to use to play some of the unrepresented classes.
With that said, there might be some ways to get the best of both worlds without completely breaking immersion. Maybe one of the new companions can potentially have a "flexible" background story that lets them take on the any class the player needs not accounted for by current companions. That companion's story just needs to be written in a way that it makes sense the player is determining their class. A couple of bad generic examples:
1) Player meets/saves a skilled but untrained commoner who gets inspired to become an adventurer. Through dialogue, the player can suggest a class/path for them to follow, and later on, you meet up in Baldur's Gate and they are now a recruitable companion.
2) Player finds a deactivated Warforge, who you can reactivate through a quest, and through it program in the desired class.
Then the flexible companion can have a proper character, story and motivations like the other companions (preferably much better than the examples I gave above). The goal is to have it make in-game sense that the players have dictated what class they are. This approach can potentially be used to let the player choose the class of some of the datamined companions too.