It has indeed been confirmed (by Steven Spielberg no less) that Staff of Kings (the next proper Indy game) will contain scenes from the movies. I think that's the best you're going to get for now. At one point LucasArts was ready to make many Indy games, with their last president Jim Ward even saying they could have an Indy game a year - where game versions of the films would have probably been inevitable. Fat chance of that now though.
There have been plenty of Indy games on the old 8 and 16 bit systems from the original trilogy. I prefer a new original story though. That said, I have zero interest in the LEGO games, and agree, if you're going to do it, do it right!
I personally would like to see a video game of Raiders, Temple of Doom, and the Last Crusade. One in which you can be other characters OTHER than Indy, like the villains