For me, Indy in Raiders was a fundamentally serious guy
I agree, but it seems like there was an underlying passion for life -- Indy loved the adventure. There was also a wry take on the dangerous situations at times. My limited knowledge of Crowe's work suggests he doesn't convey that same joy of life; his characters have been more embittered. If Crowe can also do lighter stuff, then I think he could be a good Indy.
Someone mentioned Zorro -- Antonio Banderas could do a decent Indy, I think.
But in the end, Harrison Ford is Indiana Jones. Recasting Indy would be like doing another BTTF without Michael J. Fox. Just not right.