The problem with saying that there have been deaths in the US but not in the UK is that the UK is a relatively small sample size and these products are fairly new to market - they have been introduced within the last 10 years. I don't know exactly when they first came to market but as I said before - they weren't around with my DC1 in 2008 but were with DC2 in 2018. I have a feeling Poddle Pod was the first one in the UK - which I can trace back to 2013 - but having not had small babies between those two years I may not have been paying attention. When DC1 was tiny there was a product called Snuggle Nest which was a hard sided in-bed co-sleeper product. This was recalled.
According to an ANEC report there has only been one death relating to cot bumpers in the UK over the last 10 years. (16 deaths in the US over the same period). Does that mean that cot bumpers are safe? No, it probably just means that sudden unexpected infant death is rare and there are relatively few infants in the UK using cot bumpers.
The problem remains that there are no safety standards for baby pods/nests and they tend to incorporate padding near to the baby's face, which is a known hazard for other products, so there is no reason why it would be different for these new products. "Breathable" as a product description has no legal status and does not necessarily mean that a product doesn't impede breathing or airflow. The ANEC report is looking at creating safety standards that these products would need to conform to going forwards in order to be allowed to state they are safe for sleep, which I think is a good idea.
American babies aren't significantly different from British babies - I am not sure why it's significant in that case that no babies have died in the UK when using these products? Unless it is relating to the way that they are typically used. As I understand it, in the US safe sleep messages focus on keeping the cot absolutely clear, even blankets are discouraged, but also prohibit co-sleeping as a very dangerous activity. Therefore these products are marketed in the US as a way to make co-sleeping safer. Parents are more likely use them in the bed rather than in cribs and cots.
OTOH British safe sleep messages, although it's also emphasised to have a clear cot, the messaging is not quite as strong in this area - items such as blankets are considered safe when used correctly and co-sleeping is not completely taboo, there was a study done a few years ago saying that completely banning co-sleeping leads parents to do so secretly without advice from health professionals, leading to more unsafe co-sleeping practice. So instead there is advice around how to co-sleep in the safest way possible. As a consequence these products are not marketed as co-sleeping products (although some people use them that way) and they are more widely used within cots and cribs.
In terms of being riskier than co-sleeping - co-sleeping is inherently risky, particularly for young babies, because adult beds are not designed for infants and contain several hazards which must be mitigated. However, if you do mitigate these hazards (no drunk/intoxicated/medicated adults; no older children/pets; bedding away from baby; parent in the protective C-position; ideally breastfeeding mum, which is a combination of breastfed babies being lower risk overall and BF mums' typical behaviour and positioning of baby in the bed, possibly something hormonal to do with lighter sleep and frequent arousal; baby secured against falls and entrapment) then there is no/only slight increase in risk compared to a cot, which is designed specifically for infant sleep and which you have to do/add things to to make it unsafe.
Source: Multiple, but BaSIS have some good summaries - use the links on the sidebar to see older studies
www.basisonline.org.uk/hcp-research-summaries-2014-2016/
So the problem with using a nest product when co-sleeping is that you are not actually mitigating several of these risks.
If an adult is so drunk/tired/medicated that they would not notice rolling over onto a baby, a pillow is not going to make the baby more noticeable.
When these products are used, babies tend to be placed in an unsuitable position for example between the parents, often between the adult pillows, not within the protective C-shape that a breastfeeding mum typically makes. This is a problem because it makes it more likely that the baby will roll unnoticed into other bedding or become covered by adult bedding as the less-aware adults move and shift during the night. It is also possible (suggested by sleep studies and anecdotal evidence) that parents co-sleeping in the C position have a higher awareness of their baby's temperature, position and general well-being which is thought to potentially have a protective effect against SUDI, and may be why co-sleeping even though it is obviously more hazardous overall does seem to work out at around the same risk level and/or even a lower risk level after around 3-4 months of age (different studies seem to find the tipping point variously around these ages)
There is likely some correlation between bottle feeding and use of the products in bed, because the advantage of co-sleeping for breastfeeding mothers is easy access to the breast. In a baby nest the baby is no closer to the boob than they would be in a separate sleeping space next to the bed.
Lastly, in addition to these three hazards which are not being mitigated the sleep nest in itself introduces the hazard of suffocation and overheating as discussed previously.