They completely bypass the intended experience of old games. Why would I ever be scared of dying in Super Metroid and going back to the last save when I can just save state before a boss fight? Or, if the emulator allows it, I can even just rewind after every minor mistake.
I know the obvious counterpoint is that you can just not use save states, but their very presence changes how you feel during play. What should be the default experience now feels like a self-imposed challenge, and the temptation to give in and use save states never goes away.
I like emulation overall for how it makes retro games more accessible, but I wish the save state had never been invented.