For the research focused, there are some references in my blogpost here on what kinds of computational problems minimally require how much CoT to solve: https://blog.wtf.sg/posts/2023-02-03-the-new-xor-problem/

Notably Will Merrill's work: https://arxiv.org/abs/2310.07923

As for how universal transformers (looping transformers, but everyone has since forgotten prior work) will affect this, Will Merrill (again) has a paper here (https://arxiv.org/abs/2503.03961) that discusses exactly this.

The original universal transformers is called "universal" because if you allow for per-token looping decisions, it can theoretically be Turing complete without needing CoT (some nuance here about levels of precision used).

As for whether having little or no CoT is "unsafe": It isn't clear that the model's CoT reveal how they actually arrive at the answer. As an example, what if they provide an answer before the CoT? (https://arxiv.org/html/2603.01437v2) If this is already in question, we shouldn't be relying on the CoT for monitoring the model's reasoning.

As always there is a lot of nuance to the topic once you get your hands dirty with the details.