I'm a bit puzzled why you couldn't extract useful information even _without_ a control group. Let's say we have a disease that we know that kills you. If you take the treatment and you don't die, we have pretty damn' positive evidence it works. The control group is the... You know... Many other people that don't take the medicine and die.
This is probably a good indication, but you do not know if it is the pill that is making the effect. It may also be the placebo effect.
It may also be that on day 6 you get better (no matter of you took the pill or not), and then worse on day 20, but much worse than without the pill.
Still, this is a statistical wink so to speak (paraphrasing xkcd (https://xkcd.com/552/)).
To be clear: I am all for patients experimenting on themselves when they do not have much to lose (and whenever they please, but they have to take their responsibilities then). Plus euthanasia if the experiment goes south.
