The SD is there have been various studies and neither sucralose or aspartame have been shown to be meaningfully harmful.
Honestly this issue comes up a lot because, as you note, there is a very large movement of people who seem to think artificial sweeteners are literally some sort of poisonous warfare agent that have, through corruption and/or lax oversight been allowed to go onto the market.
If you look at this catch-all Wiki page on sweeteners you will note that pretty much all of the major ones have been studied not dozens but hundreds of times by health agencies spanning the globe and no materially adverse effects have ever been linked to human beings.
Unfortunately I think part of the fear is spurred on because of grave misunderstandings that have come about in the past.
For example an artificial sweetener anyone alive in the 70s may remember, saccharin, was widely assumed to be bad for you for a long time. In the 70s Canada banned it for human consumption based on laboratory tests done on animals. The FDA in America was moving to do the same, but Congress stepped in and blocked it. For ever onward people have fueled their conspiracy theory fires against artificial sweeteners based on this action.
In truth, the study linking saccharin to cancer was done on laboratory rats and subsequent research has shown that it causes bladder cancer in rats through a mechanism that does not apply to the human body. Something many people need to remember is, just because rats are commonly used to test thing on, and just because they are mammals, there is not a 1:1 relationship between how things affect different species and how things affect us. There are many mammals that can and do eat things that would cause serious adverse effects in humans and vice versa.
So even the one artificial sweetener that has been genuinely banned by some countries, extensive subsequent research and the WHO has concluded it is safe for human consumption.
When it comes to the mainstream sweeteners used in consumer food products today (sucralose/Splenda and aspartame/NutraSweet) about the worst thing you can genuinely find is a few studies have shown they can cause cancer in rats. However again, both substances have been vetted and OKayed by hundreds of scientists and health organizations all over the world. As has been shown with saccharin just because something is a carcinogen in rats does not make it a carcinogen in humans. Further, the dosage in these studies that have found any problems with rats is insane. For example a study showed that Splenda can kill good gut bacteria in rats. The dosage for that study was the equivalent of consuming something like 10,000 packets of Splenda or many, many thousands of sodas or coffees worth of Splenda in a single day, every day for a period of time. I would posit far worse side effects would present if a human was consuming that much coffee or soda per day and from things other than the sweetener, think about how much caffeine would come with that many coffees or sodas.