Both videogames and anime are visual mediums, they always have "graphics" because without them we'd just have electronic books and drama CDs. The particular nature and style of the graphics is dependant on the creator and what they're trying to convey or make the viewer/player feel. Some modern games use the power of the computers/consoles to try and be as realistic-looking as possible because they're trying to make the player feel like they're in a real situation whereas other use it to create interesting styles that weren't possible on older machines.
Okami used the processing power to create a world that resembled
sumi-e artwork, to enhance and play on the mythological nature of the plot and characters and to also give a root to the paintbrush gameplay mechanic. If you played as a photo-realistic wolf in a totally realistic setting, the whole game would have felt different despite technically being the same game. Same as how the nature of the game would change if you played as a cel-shaded soldier in a cartoon world in Call of Duty.
So in that way, Lucky Star is using the supposed cuteness of the characters to appeal to you. It wouldn't work if the cast was all male and drawn like
Akagi. Boogiepop Phantom is trying to make the viewer feel like what they're seeing is really happening, not just some fantasy tale. It's also meant to be very unsettling. It couldn't use the Lucky Star style to achieve this so instead it draws the cast realistically (comparatively speaking) and gives them more Japanese features like black hair and eyes rather than various blues, pinks and reds.
Trapeze is meant to be playful and surreal; the art-style captures this. It's meant to be about how the mental problems of the various patients are changing their perception of reality so the anime uses various levels of realism including live action actors, rotoscoping, 2D but with more realistic facial proportions and more typical anime styles. The style isn't usually separate from the substance but rather contributes to it. All anime has made a conscious choice about it's art style based on the style of the show, the feel of the show. Whether it's cheap and cheerful or "pretentious", a stylistic choice has been made for the same reasons.
Fenex wrote...
There just following in suite of the video game industry if you havent seen story< graphics now days
its sad
Yeah because old classics like Pong and Space Invaders were very story-based unlike modern crap like Metal Gear Solid, amirite? Look at series like Final Fantasy and Dragon Quest, and the games tend to get more story-based as they go on. The same is true even for not particularly story-centric games like FPS; compare Doom to Half Life 2.