That still gives 50-50 odds with sufficient sample size, not much of a test of the research hypothesis (since many alternatives will predict the same direction). It is better than 100% chance of rejection though.
Couldn't you make an argument that the point H0 has use when you are testing whether two populations are identical? i.e. it's probably true that \mu is very close to 0 if it is the difference in heights of men from Nebraska vs men from Iowa.
You've kind of hit the point with the second half of your comment. Two populations are virtually never identical, so you don't need any statistics to answer the question. A more reasonable question is whether or not you have the statistical power (i.e. measurement precision) to see the difference, and whether the difference is big enough to matter.
However a composite hypothesis setup of the form
is probabilistically sound (in as much as some journal requires you to report a p-values). Much better to report effect size estimate and/or CI.