Doesn't a curve tracer harm modern circuits?
While you can hook up a simple LED or capacitor and get a nice graph out of it, won't any modern IC be damaged if you put -5V (AC) through its VCC rail, even if low current, considering that most ICs have a very low reverse voltage maximum rating.

You're right. You can't use this testing method, neither safely nor sensibly, for just arbitrary circuitry.

I saw a couple of videos of people testing and making whole databases from a single board, but isn't that playing russian roulette, in a way? In the motto of: &quot;Let's put AC through until something breaks?&quot;

Videos (esp. Youtube) are a usually a pretty bad idea.