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.