I'll assume that by "spayed" you mean getting the tubes tied. But we don't use that word for humans, so please don't go around saying women are spayed.
Tube tying only prevents pregnancy. It does not prevent any other problems like cancer, cysts, infections, or endocrine-related issues. Removing organs can cause hormonal issues, and generally there will be more side effects from removing the ovaries than the uterus.
Lots of women don't need to see a gyno that regularly, but doctors have decided that's the best way to collectively prevent certain types of cancer. We're not as worried about cancer in pets, because they don't live nearly as long as humans.