Aren't you forgetting GIF? Not a great format admittedly, but in photoshop there's even a "lossy" slider.
Photoshop uses the same tricks for "lossy" gif that this article uses for PNG.
LZW is just a very poor compression. Even best case is taking ridiculous amount of bits (you can only add 1 byte to previously used pattern, so it's sequence of symbols for 1+2+3+5+6+etc. pixels resetting every 4k iterations), so there isn't even room for improvement.
So, GIF is awful. Should be forgotten.
8-bit palette and crappy compression do not matter when you offer exclusive features.