>I have always wondered if hybridization wasn't actually more commonly possible.

It's incredibly possible. It happens all the time. The only reason you think it doesn't is because the definitions of words.

The entire concept of the taxonomic tree is human made arbitrary decisions. By definition, when hybrids are "common", we group them together as one species.

But like, pretend you are an archaeologist going through bones. Would you call a Chihuahua the same thing as a Rottweiler? That's totally a hybrid. There's so many, we call them all "dogs" and just use a different word: breed.

If that doesn't convince you, look up Ring Species, which are incredibly cool and totally make you rethink how you think about species.