This is a near universal consequence of academia's incentives and extends into many of the sciences (although biology is most susceptible due to its complexity).
[1] http://www.nature.com/nature/journal/v483/n7391/full/483531a...
[2] http://www.nature.com/nrd/journal/v10/n9/full/nrd3439-c1.htm...
It is not simply a matter of incentives (although they play a part). Another issue is pure publication bias. If you get 'landmark' results, a paper is much more likely to publish then if you got the results everyone would expect. In many ways this is one of the necessary functions of the journals, as it allows people to look at the new stuff without sifting through many articles of expected stuff, but it does create a bias.
Add to that the incentives of needing to get published, and constrained resources, and a willingness to publish what could be sub-par methodologys (of course they are par), and it is clearly not the best system.
Every journal publishes novel and statistically significant findings, and probably encounter similar rates of type 1 error as Nature and Science. It's just that Nature and Science are more susceptible to human politicking and don't seem to face up to it.
Prestige is a relative thing, and there's nothing more prestigious than Nature (or Science). Your suggestions are good, but I think they would be more likely to be adopted first by a journal that isn't Nature or Science, that possibly wanted to compete with them.
I hope some lesser journal becomes greater, and soon.
These high profile journals serve the purpose of publicizing discoveries that are thought to have far-reaching interest in science. However, at the same time, they have the strictest limitations on publications, meaning that the methods section, the foundation of science, are rarely described in any detail. So they have some of the worst practices for publication while supposedly chronicling the most important discoveries.
So while Nature/Science papers make the news and make people's careers, it's important to downweight the certainty of the finding until there is independent verification.