I don't think it's always a budget reason but sometimes comes down to preferences or narrative choices. If you have the companions butt in on everything, this might be more realistic but narratively it draws attention away from the main situation. The Shadowfell is Shadowheart's scene so the focus should be on her. I think a scene that handled this really well is Gale's orb reveal, during which you can ask your companions about their opinion on the matter. It keeps the focus on his situation but allows the others to voice their opinions which makes it feel like a group decision.

The high stakes dice-rolls, I think, are often added to give some excitement to the scene, like you are in the hand of fate. And I get the impression that a lot of people really like that. Personally I don't, it's often a cheap way to get a dramatic climax opposed to having to write a dramatic dialogue. Though it didn't bother me too much in Shadowheart's case, for me easily the worst offender is talking Astarion out of the ritual. That scene is such a waste of some excellent build-up and all of it's "excitement" hinges on that stupid die roll. - On the other side you have Gale's amazing boat-ride which is pure dialogue with no gimmicky rolls at all. Just a long conversation about how the two of you want to proceed with your lives, very beautifully dramatic with excellent player dialogue that gives you a great deal of range in your replies, but it is also a very calm scene.

Also, I really like the playable origins. I wouldn't have finished the game with a Tav or a cringy horror-for-people-who-don't-like-horror Durge, but I absolutely love it when taking up the mantle of one of our pixel-friends. Astarion's whole story is so much better if you play as him and Gale's gives you such a unique perspective on things, and I love how everyone just treats you like a bro and doesn't coddle you overly much. My Shadowheart run was spoiled a little by forced player-prioritisation for which I hope there will be a better solution in future games. (Having Astarion, Gale & Bae'zel do the talking for me, felt like such a Sharran approach.)

PS: Not talking about act 3 here which probably really suffered from lack of baking time.