Interesting thought, but the situation is more complicated so it might not work that simple.
About EU, there's one very important factor - US provision of security umbrella to all its members including Germany after WWII - and this makes integration easier for all members despite all their differences. Russia is isolated out of the picture, Pax America.
Now take a look at the Asia Pacific, and imagine there is no PRC, then it would be another EU right? Japan the leader country, Korea and TW as equal partners, then so on and so forth. So again, Pax America.
But the reality is China is in it. Biz-wise it's not out of the picture like Russia, rather it engages deep trade ties with all members of this region. Security-wise it's not like Germany, China's has its own geopolitical plans. So China is Russia + Germany? Or what is it? Sinosphere is more complicated than it seems, don't leave out the US factor. So the EU way (even with the magic formula you suggested) can't apply.
Further more on your magic formula, addition of India, doesn't solve the problem. I don't undermine India's weight, I do appreciate them as an important country, but the China to India weight ratio is a lot different from the Germany to UK weight ratio. Also, bringing India alone into the picture is incomplete, you should consider bringing the whole S Asia into this. But then I think the whole big game is so complicated that at least I can't figure out how to play with, worth exploring though.
Its an interesting and worthy point of conjecture tho -- to consider the plausibility of greater integration of South Asian - ASEAN - East Asia. Definitely would require us to read more into its strategic depth.

China may have as priority economic development(which i think they truly have for now) over military adventures or whatever, But that doesn't means they wouldn't be contained by the U.S/west or even Japan. Every rising power will always find the established power(in this case the U.S) on its way. Of course its normal, why would i cede my number 1 position to you without a fight/effort? I will try as much to slow you/bring you down as much as i can, using any means, it doesn't matter how dirty/illegal those means might be as far my objectives are met.
), we and France also fought for colonies all over the world,The U.S did same with the Soviet Union/U.S.S.R until it collapsed
, the U.S even tried to do same with Japan when the yellow peril from the east was 'rising' and 'wanted to take over the world' during the 70s and 80s. So with China it won't be any different, im sure even Japan won't be happy to see China dominating Asia, so it will also try and do what it can to deny it this by any means it can. Even when/if India, Turkey, Brazil etc becomes too big and powerful tomorrow like China is then believe me U.S will also treat them the same way. It has nothing to do about democracy/allies/partners or whatever. It has to do with interests and supremacy. So don't expect everything to be merry like on this article.lol I cant say it enough, geo politics is never clean, its a dirty game, you just have to know how to play it.