We've had discussions before about the idea/concept of an Indy reboot. But is it really a viable idea? A franchise like Bond or Batman can potentially be rebooted forever in different styles as they're not really stuck to any particular era or actor.
Unlike Bond, which doesn't have a real time line or continuity and exists in a universe wherein the character never ages, Indy films are as much (not serious) period pieces as they are adventure films, and the role is very much tied with Harrison.
If Harrison had retired from the role with ToD or LC, he could've perhaps been replaced had if a good enough actor had been found soon after. Like Sean Connery only spent 5 years in the role of James Bond and yet he's STILL arguably the definitive actor in the role--He's in some people's eyes never been truly replaced in any perfect sense. But Harrison has had the role of Indy for 30 years; it's his.
I honestly have a hard time believing that any actor, regardless of how good they were or how iconic they themselves were, could ever successfully replace Indy in the eyes of the public. The actor and film might be good, great even, but I don't think the public would swallow it.
However, if they did do a reboot, they could just totally rewrite the continuity afresh ignoring the originals and potentially make lots of films set from the 20s to the 50s. That could be possible I guess. Get a young guy and make like 5, 6, 7 or more films spanning from 1920 to 1960s or something. But therein lies another problem: Unlike Bond films, which are usually pumped out every 2-3 years, Indy stories and films take a long time. This could be avoided, however, by using existing material (IE the novels, comics, video games) as a story basis for films. Most of the early Bonds were themselves based on Fleming's novels.
So it's kind of a wishy-washy proposition. If they go at it the way I laid out in the last paragraph, though, it could IMO be great. I mean is there anyone who wouldn't want to see Fate of Atlantis adapted to the big screen? Or one of the Bantham novels? Or Infernal Machine, if done right? There is a treasure trove of stories.
The major problem I see with this ever coming to be is George Lucas. Not only do I doubt that he'd EVER hand over Indy (story-wise) to someone else, but he doesn't seem to have much interest in the character anyway, at least compared to SW. And I don't think he'd ever allow an Indy film to be made which was based on a story he didn't write. He wouldn't allow an Indy film with the credits "original story by Max McCoy" to come out--Just because of his ego/desire for total creative control.