I’d guess that lack of REM would cause symptoms like daytime drowsiness, but it’s the physiological effects that are gonna kill ya.
My understanding is that bad sleep will induce chronic stress and chronic stress will induce high blood pressure.
So yes, bad sleep will dangerously increase blood pressure but it’s not a direct effect.
(That’s my interpretation, maybe it’s false)
In fact it turns out that REM sleep can sometimes compensate for apnea in some people, that is, the onset of REM can happen more quickly. Some people can get enough REM sleep even with apnea.
To be clear, ultimately all of these things can become problems, I’m just disputing that lost REM is the main health concern. It’s one concern, but AFAIK, in the long term venous damage is what will kill you.
To expand / clarify slightly: REM sleep is absolutely essential to "higher animals". It is not, though, "deep sleep" in the sense that "long slow delta wave" sleep is often called "deep sleep", and the "NREM" stages of sleep tend to be "deeper" (in the sense of physiology 'slower' / harder to awaken) than REM sleep.
This Wikipedia article could use some editing, at least for clarity, but is certainly a solid enough reference and starting point for further reading (for anyone interested): https://en.wikipedia.org/wiki/Sleep_cycle
Apnea is incredibly stressful on the body / mind. Disruption before REACHING REM sleep (one of the reasons REM may be referred to as "deep sleep" in non-technical language) is among the worst of the effects. Since most of a single cycle is NOT REM sleep but rather stages occurring before REM, REM is a phase most often prevented by episodes of apnea. But, the physiological stress also relates to disruption of other phases as well.
Besides sometimes profound effects on cognitive function varying over days and weeks depending on the severity / frequency of "apneic events", the stresses that accumulate over time tend to cause cardiovascular problems, especially.
As usual, sites like Cleveland Clinic's and Mayo Clinic's etc. give good info (short of the more technical scientific review articles you can search for on PubMed, for example). Cleveland Clinic's seems quite good to me (perhaps a bit better in clarity regarding phases of sleep than the Wikipedia article, as well):
https://my.clevelandclinic.org/health/diseases/8718-sleep-ap...
Edit: you wrote "long deep REM cycles" - that's a reasonable phrasing and would also 'frame' effects overall. So, if it's unclear from my writing (ha, write after I 'dinged' a Wikipedia article), there is no conflict (depending on exactly how one reads these messages, of course) between my message and the parent. To clarify, it was not my intention to come off that way (but I see that certain emphases might suggest that, apologies if it reads that way to some!)
