Unfortunately, it is hugely over simplistic. Using it you can conclude that blackberries and raspberries are the same species and that lions and tigers are kinda-sorta the same species, since it has been possible to get Ligers to successfully mate with their parent species.

So regarding its characterisation as "a very simple scientific test" - no, it isn't.

There are even not-uncommon situations where Population A can breed with Population B, and Population B can breed with Population C, but Population A and Population C can't interbreed.

Using "can breed" as the metric for "same species" creates the situation where A and B are the same species, and B and C are the same species, but A and C are not. That's clearly contrary to what most people have in mind when they use the word "species".

Species really should be a continuum rather than a binary.

Polar bears and grizzlies are probably a better example. They produce fertile offspring but no one thinks of them as the same species.

Wolves, coyotes, domestic dogs are another example that comes up in this discussion.

Yeah, all of those can interbreed, more or less. On the other side of the coin, consider dogs alone. Successful breeding between Great Danes and Chihuahuas is quite rare. :-)

The "successful breeding" metric isn't very satisfactory on any level

In high school. Once you take a slightly closer look, it completely fails all over the place (ring species, asexual reproduction, etc etc).

See also https://en.wikipedia.org/wiki/Species_problem .