Branching would be really tricky, but there's no physical barriers. Note that even Musk's proposal isn't as far as you can take the concept. If you fill the tube with very low pressure water vapor instead of very low pressure air (via more pumping to overwhelm leaks, plus water vapor injection), your top speed jumps 40%. Fill it with hydrogen and it jumps 300% (normally hydrogen is a real pain to work with due to flammability, embrittlement, etc, but the densities in question are so low that such issues are mostly avoided). So we're talking the potential for hyperloop "speedways" for long distance runs that could blow airplanes out of the water.
The low numbers of passengers per capsule is really key to making the concept economical. Compare, say, monorail track with a full sized rail bridge. The former is vastly cheaper per unit distance because the peak loadings are so much lower, because the mass of the monorail trains are so much lower. A computer-controlled high launch rate of small, high speed capsules means you're spreading the loading out greatly, which means greatly reduced loading and thus materials costs.
Still, while Musk has been thinking of Hyperloop stations in the "airport" concept, he really needs to get out of that mindset. His proposed plan had them on the outskirts of cities. Airports are only on the outskirts of cities because they *must* be. You greatly reduce your utility by doing that, by making people catch connecting trains. Hyperloop can extend just fine into towns; with his two proposed endpoints in particular there are excellent rail routes into town that are quite straight that it could be built over.