Edit: deleted distracting details that the comment below rightfully calls out.
this is the key part of your statement. Many animals for many diseases appear healthy but don't until a work up in done.
The spay and cost numbers were just examples. In general, yes, spays are safe, but it is anesthesia. There's a risk of death and it gets much more complicated with a huge variety of factors - age of the animal, species, whether she is in heat, and of course like we mentioned - pre-existing conditions that do not obviously present itself without a clinical workup. The last one is huge. There are plenty of values that are indicative of organ failure that would not be obvious to an owner. A dog can't tell you it's been having a nagging pain on its side for the past week.