A couple of problems with that idea:
1.) That requires a calculated attempt to eliminate ALL existing racial groups, aka genocide.
No. That requires biology and the interplay of human hormones. There are mixed marriages/couplings among the posters here. Would you like to poll them to ask how many chose their mate via:
A) Hmmm? I think I'll pollute the white race and lead to its ultimate disappearance. Sounds like a plan.
B) Wow. Check out the butt on that guy/girl. Gonna do some serious *********** with that if I get a chance.
2.) Some groups are far larger (and with higher birth rates to match) than other groups, currently. The resulting mixed single human race would be comprised of far more of some peoples' DNA than others' and those who had bred most irresponsibly would end up rewarded for that behavior. Not to mention the fact that some groups are characterized by far more dominant traits and others are characterized by more recessive traits which means that even if the planet were comprised of exactly 3 billion whites and exactly 3 billion blacks, and nobody else existed or ever had, whites would have a legitimate basis to feel that some of their defining characteristics stood to be lost under such a proposal. It's true that light colored eyes, freckles, reddish hair and such don't disappear 100% of the time after one generation of mixing, but they *tend* to not show up and they also tend to get swamped and disappear with subsequent mixing, and at best appear in a very dulled and reduced form. This problem is only made much worse by the fact that, as previously stated, the groups with more dominant traits are currently far larger and this would just make the swamping / genetic destruction angle all the more pronounced.
This presumes that mere racial characteristics are something one wants or needs to see "preserved". Why? Sure, they're aesthetically interesting, but as an end unto itself, preserving the white race by segregating so that only whites will breed with whites is really rather repulsive. As would be locking-in East Asians>East Asians, Blacks>Blacks, Pacific Islander>Pacific Islanders. Your world limits people's individual choices. You are free to have your opinions and live your life as you want to. And I'm sure there are individuals in Asia, Africa, Europe, etc... who agree with you, emotionally if not eugenically, and we'll never really run out of whitey as a result.
3.) Many people (from all groups) exist now, and could be assumed to exist in the future, who would not want to take part and who wish to preserve their group. What would we do, force them to pair off with someone of a different race? How far would we be willing to go to achieve this dreamed of "zero diversity" world?
Those who don't want to take part are free, like you, to not mix their pure - for certain definitions of pure, of course - blood with the muskier races. Your ideas, though, propose through segregation and separation of cultures and races, that whether they agree or not, you'll have them making white babies,... for the good of the race.
4.) Many people (including a LOT of nonwhites, possibly even the vast majority of them) consider fully white babies/adults to be much cuter / more desirable than mixed babies. Especially when the mix is with blacks. In the nonwhite world, light skin is prized. Light hair and eye colors are prized and seen as desirable. Among East Asians, Amerindians, Middle Easterners, etc. blacks and their associated genetic traits / appearance are seen as undesirable, generally. Even within blacks themselves, these attitudes are quite common. Light skin seen as preferable to darker skin, "good hair", skin lightening creams in Africa, etc.
Culture. Media. Fashion. All those things are changeable, particularly if you consider something as elusive as aesthetics. In fact, in many cultures, it has nothing to do with innate aesthetic sensitivities but a perception of "white = power/wealth". I can equally say "many people, including a LOT of whites, possibly even the vast majority of them"... find mixed-race children exceptionally attractive. I know it'd play out in my demographic.
5.) Many of us feel we have good reason to suspect the resulting mixed humanity would be less capable of facing the challenges of the future and of technological civilization than current existing varieties of humanity are equipped to do (Whites, Jews, East Asians)
What many of you feel is of no consequence. What any of you can prove would be and there's no evidence that your purity-of-race theories hold any more validity than random chance. In fact, there's a lot more evidence in nature for the viability of diverse organisms. Check your own DNA. Probably not just not-all-white, but like many of us, there's a fair possibility there's some Neanderthal in there.
Of course, the biggest issue is that this idea is just completely pie in the sky and unworkable but I know you're not proposing it in an entirely serious manner. We've both obviously heard many other people suggest it before, so I'm just using this as an opportunity to point out some issues with it.
Unlike those of you proposing segregation and intra-race reproduction only, no one's actually proposing this as a plan. We're just saying, "let it happen". There will be a time in a few hundred or few thousand generations when the whole world is a nice cafe-au-lait color. You won't be around to see it, nor will I, but it doesn't actually worry me any more than when my ancient African ancestors moved to Europe and gradually turned whiter. **** happens.