Yes, I played with the two fish method last night, and eventually you can get all the fish ... but I wouldn't change to breeding that way. It takes more steps than the nine fish method and doesn't seem to follow as valid breeding progression, because you breed rare fish before breeding some common ones.
But ... crossing Spotanus with Stickfish from eggs might be a quicker way to get the Betas for breeding in some cases. --- but usually I don't have much trouble getting them from the eggs while collection the others.
I'm sure there are many many ways to play the game beside the way I do.
I developed my way so that I can produce the 441 in a game without driving myself nuts with random breeding.
After finding the 7 Magics and 21 Perfects, I needed more fun!
Now having breed the 441 I'm doing fish level research and genetic research. Makes me wish I'd gone into some sort of scientific studies in my younger days!
Never knew I'd love it so much!