When a geographic region is ethnically homogeneous, the (almost) only representatively legitimate solution is autonomy. Crimea was given autonomy within Ukraine. But I too wonder if a completely separate nation-state will work better for them. The danger there is falling under the thumb of Russia. I wonder if my argument applies to the American South. I also hope this doesn't become about Crimea. The protests aren't about Crimea, they're about illegitimacy. Russia is like America: they have to make sure everything is about them.
Crimea is not an ethnically homogeneous state. There are three significant populations in Crimea: 1. Russians. The majority of Crimea is Russians; they came from Russia and made Crimea their new home (although most Russians don't consider Crimea (or Ukraine, even) as separate countries; according to them, they are still a part of Russia). They are vehemently in favour of Russian rule and are against the recent events that have happened in Ukraine. 2. Ukrainians. For the most part they have pro-Western ideals and are upset about Russian intervention. Crimea is a part (simplifying here) of Ukraine and has been since 1992. By retaining control of Crimea, Ukraine has a pretty strong bargaining chip against Russia. This is the ideal solution for the Ukrainians of Crimea. 3. Crimean Tatars. Tatars are native Crimeans. They are a tiny population of Crimea because of the ethnic cleansing that happened in the 1940s. Most Tatars that were deported died on their way to Central Asia. Due to the small size of the Tatar population, nobody gives them any mind and they are generally ignored while Ukraine and Russia fight over their country. The problem should be easy to see. Crimea "belongs" to Ukraine. Its population is mainly Russian, who wish to be a part of the Russian Federation. It lies in a geographically important spot, mainly for economic and trade reasons. There are countering ideals of pro-Western and pro-Russian people. And the most important part: Ukraine, Crimea and Russia have a history of being very violent locations. All of this baggage exists in this part of the world. But let's not forget about the EU, NATO and the US. There is no easy solution to this.
Sorry, I didn't mean to imply there are no minorities in Crimea, or that they shouldn't be represented. All nations have minorities, and all democratic governments need provisions to protect them from oppression. What I meant was that, as you say, "its population is mainly Russian," which is disparate from the rest of Ukraine. Perhaps I should have said, "Geographically distributed demographics ought to be governed separately."
I see what you're saying, but it's too much of a clusterfuck for any sort of sane solution. Many Russians don't see post-Soviet countries as being separate from Russia. There's a similar part of the population that has no desire to assimilate into local populations. What ends up happening is that there are many Russian enclaves all across eastern Europe that want a Russian-friendly home. This is Crimea, Southern and Eastern Ukraine and other post-Soviet countries. As a consequence there is a Russian cultural empire growing in non-Russian countries. So letting the demographics decide the governing body is how the Russian empire spreads across all of eastern Europe and the Middle East. Not great. But as I said, there is no sane solution. My solution is to throw my hands up in the air and hope there won't be any bloodshed.