I don't know much about Cronbach alpha but my guess is that there's no mathematical reason that .7 is the cutoff. There are a lot of 'rules of thumb' when it comes to cutoff values and there's no reason for most of them except that at some point somebody decided it was a decent value to use.
Alpha of .05: We get this because Fisher one time said that an observation that is more extreme than what we'd see in one out of twenty cases should be considered significant.
VIF > 10 means multicollinearity (some people use other values): Totally empirically based (and the fact that variables giving an R^2 > .9 can give us a VIF > 10). You can do whatever you want with this but it suggests there might be some issues with correlation among the independent variables.
Sample size greater than 30 to use a t-test on nonnormal data: Slight application of the CLT but 30 is nowhere near infinity. Mainly based on observations that for data that is even somewhat skewed the sampling distribution of the mean is approximately normal.
So I highly doubt that .7 is truly a magic number. But even though I don't know much about Cronbach's alpha my guess is that it's a decent rule of thumb that has been probably studied empirically.