Aspartame has been tested like crazy and does not have any known dramatic effects on health. As you mentioned, it's very sweet per molecule, much sweeter than most other artificial / sugary sweeteners, and so you don't have to use very much.

Some other artificial sweeteners, like saccharin, aren't nearly as sweet per molecule, and you have to add a lot to get the desired effect. They also have an apparent effect on glucose intolerance related to one's gut biome, and it's not due to the taste - you can transfer the biome alone between mice and get a similar impact.

Example source: https://www.nature.com/articles/nature13793