So that leaves language level support. So far the only contender that I can see coming up is Julia - and it will take a lot of effort until it can reach performance levels on par with Fortran. This basically would require a big push by one of the big software companies - who all aren't making a lot of money in HPC software anymore. I could see Nvidia picking up the ball at some point, it would suit them well - but then we're getting into vendor lock-in again.
http://en.wikipedia.org/wiki/Row-major_order explains it nicely.
If you wanted to take a native Fortran matrix and turn it into a native C matrix, you'd either need to copy everything to re-arrange the in-memory layout or do funky things with the indexing. Neither option is great.
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Bringing it back to a higher level, I'd agree that your point makes sense most of the time. In most cases, the cost of a memcpy(3) would be a rounding error. That's certainly the case for most web applications. In a tight loop in a math-heavy application, though, the standards are a bit higher.
In theory, sure. In practice a bunch of languages have tried and yet Fortran is still the king.