I think IPSC or IDPA or similar events have a better chance than benchrest, at least from an audience excitement point of view. Plus, just listening to the anti-gun folks rip their hair out because they are shooting at targets that look like people would be worth the price of admission.
IPSC and IDPA can NOT get an event into the Olympics. Shooting events MUST be sanctioned by the ISSF and no one else.
The last new-on-the-scene shooting event that had a chance to be added to the Olympics was handgun silhouette, way back in the late 70s and early 80s. It grew to over 10,000 participants in the U.S. over the space of just a few years. There was significant interest around the world and there was even the beginnings of spectator support, as crazy as that seems.
But IHMSA (which, at that time, was essentially just a business belonging to one man) refused to give up control of their rules and procedures to the ISU (now ISSF). Despite the fact that a worldwide body did form (the IMSSU) that could have worked under the ISSF umbrella, the loss of the U.S. contingent meant that the sport lost all momentum on the world stage. Not coincidentally, the sport also lost momentum in the U.S. due to a number of factors, specifically including the death of the man who ruled it.
Since WW2, shooting sports have come out of the Olympics. None have been added. There's been some gender-specific shuffling of events (Boy, was that a mess back in the 1960s and 1970s!) but nothing has been added. Free rifle is gone. Running target is gone.
There are really only two reasons that shooting stays in the Olympics. First, the founder of the modern Olympics was a pistol shooter so there's a strong tradition. (Did you know that the first medal at the Olympics, by tradition, is awarded to a pistol shooter?) Second, shooting is something that any country can be competitive in and, thus, it has a broad base of support. In how many sports, for example, do Serbia, Ukraine, Croatia, Qatar, Belarus, Slovenia, Slovakia and Cuba have a chance of winning a medal like they did in London? The IOC likes to spread medals around to plucky underdog nations; it's good PR. Shooting fills the bill on that.
Unfortunately, as the Olympics turns exclusively into a massive marketing machine, sports without big sponsors will suffer. The ISSF is changing match formats to make them more TV-friendly and, thus far, they haven't really succeeded. The notion of benchrest going into the Olympics is kinda off the radar of Olympic shooters and administrators; they're more worried about keeping
any shooting in the Olympics.