Actually, there already is a form of anime -- though it's not exactly animated -- that uses nothing but static pictures. I think they're called "gekiga" (this term also means "dramatic pictures" as in serious, non-escapist manga). They're basically made by filming the actual manga panels and adding a soundtrack. I've never seen one, but I imagine they're pretty dull to slough through; however, several major manga (such as GOLGO 13 and the original '60s ninja story KAMUI) have been adapted this way. "Comics with soundtracks." It's an art form, or a curiosity, that seems to have been more widely used in the past and died out in the mid-'80s.
Anyway, I think one of the reasons which anime has its moments of stillness, admittedly, is because of very low budgets. Anime, particularly television anime like EVANGELION (or DRAGON BALL Z... television anime is a broad umbrella) is produced pretty cheaply. However, it's a conscious choice: concentrate on a few important action scenes or movements, and let the rest of the movement be implied. In American animation, the tendency is usually to have a fairly constant amount of not-particularly-dramatic emotion, such as walking scenes. (Particularly since a lot of American animation, until recent years, didn't break out of the 'ant farm' look of, say, SCOOBY DOO or SOUTH PARK -- people generally move and exist on a left-to-right plane, with no effort to use dramatic cuts like you'd see in real movies. Maybe these comedy shows are mimicking the 'studio set' look of sitcoms. God knows why. I would say that this is going away, but it's resurfaced with all that Shockwave Flash animation junk.)
Of course, some anime -- a _lot_ of TV anime -- looks pretty cheap and is clearly skimping on the cels. I wish some of the money that POKEMON has made would be poured back into making the movies look less embarrassing next to their glitzy American-feature-animation competition. But there's no need for everything to be constantly moving, and if you really wanted to see comparable animated features, you should compare shows with approximately the same budgetes.
And of course, EVANGELION totally rocks either way, even if they do run sort of low on animation towards the end...