There's a few reasons. But the biggest ones involve not having to use new land - not out some sort of idealist reasons, but pure economic practicality. First off, you need right-of-way. This is expensive. Also really ticks off land owners if you have to use eminent domain. These things almost always get tangled up in the courts. For in-town legs it'd be even harder. Secondly, all new projects have to go through a series of impact reviews. If you're building over a highway median, you're in an area that's already passed review - you still have to defend your incremental changes, but you don't have to pass as much of a barrier.
Also, most people overestimate the cost of the columns, comparing them to the cost of rail bridges. Just ignoring that by their very nature rail bridges are generally only built over difficult areas, and are going to be extremely price, It's important to note that one of the key cost-saving measures designed into Hyperloop vs. rail is often overlooked: weight. Hyperloop vehicles are more than an order of magnitude lighter than a passenger train, and only spend a brief period over any given segment; consequently the required structural strength is dramatically lower than for a rail bridge. I did some quick calculations, including tube mass, and found that and Hyperloop loadings should be similar to that of Disney's monorail. So think columns like this, not this.
While I do have criticisms for Hyperloop, I found that a lot of the criticisms levied against it on the net were seriously misguided, using ridiculous cost comparisons (another one is comparing the cost of Hyperloop tunnel boring to that of boring tunnels over an order of magnitude larger). I dug up "comparable" projects for each step of the project, and I really have to say, Hyperloop's numbers don't actually look to be that unrealistic. The keys of right-of-way reuse and low point loadings offer serious cost savings.
That said, I think Musk's positioning of the concept was stupid. By putting it in competition to an already-controversial high speed rail project, he both invited the rage of rail fans (who are used to feeling as if they're under attack), as well as inviting the expectation that it can do everything rail can (including, for example, making many stops along the way). It really is, as it was billed, an intermediary alternative between high speed rail and air travel - in speed, in throughput, in ability to make stops, etc. Consequently he should have proposed the first major project of it to be LA to Vegas. Then he wouldn't have encountered opposition from high speed rail fans, and the route doesn't have much population along the way to service. Plus, he could probably get tons of private backing for such a project, as Vegas is always desperate to better connect itself with customers in California.
I also think that for the current proposal, Musk should have positioned the LA station further into town. He's thinking "airport", and of course you can have local train / bus service to the station wherever it is, but airports are only on the outskirts because they *have* to be, mass transit is really ideally located more in-town. And there's no reason that he can't continue into town - the roads get a bit curvy but there's some nice straight rail lines that they could go over straight into the heart of town, and that'd probably be even easier to get approval for than for over road.