In theory, one setting on the TV should be enough. In practise though that's rarely the case. Something as simple as the ambient lighting level affects the basic picture setting for brightness, and that then has a knock on effect on colour and possibly contrast too. So it would be perfectly reasonable to have one mode for daytime viewing and another for night. There's also differences in how progressive images are handled compared to interlaced. To be fair, a decent TV should do a fairly reasonable job of detecting the video cadence to tell if it's an interlaced or progressive source, but that's not always the case.
Coming back to your question about animation versus live action for movies, that's simpler to answer.
Film studios have a set of standards they work to for picture. The basics of those standards define the black and the white point (dynamic range), the range of colours (gamut) and the relative image brightness as the picture goes from dark to light (gamma). Even allowing for creative decisions about colour palette e.g the matrix green tint, or hyped-up or muted colour for effect, then all film output should conform to the picture standards laid down for the industry. So one TV mode should cover everything from animation through to film noir. Certainly when a TV is calibrated correctly then that's exactly the situation once ambient lighting is taken in to consideration.
My own TVs are all set with picture modes for day or night viewing. The exception is my lads TV for gaming. We have that set with additional modes for below black to handle games that use a 0-255 dynamic range.
