Of course it should, but that was originally the intention of the Chronicles, to go right up to Temple, we'd see Indys first day as a college professor, why he decides to always have a whip on his belt, where he got that leather Jacket, which time traveller gave him a 2nd world war gas mask bag.
In fact, I think the reason they never used the raiders march in the bits we have is because, like Casino Royale's use of the bond theme, they were building up to it.. imagine, the first time we see Indy in full indy gear, the theme thumping from the speakers... theres indiana jones...
Also, recently theres been the revelation that it was planned for Remy to die of thirst in his search for the peacocks eye, imagine how much more cynical that would make Indy?
I'm saying alot here, but regarding SPF, he did a good job, I guess, but much of the character consistancy would have come down to him, as an actor myself I know that it doesn't matter whats going on in the script, you can make any line of dialog suit any character. Think of all the ways one could say 'I hate snakes jock, I hate 'em' terrified, petulant, humorously, ironic, the way Ford says it, screaming it out, angrily, unbelievably, makes Indiana Jones.. he makes it a truism.. an angry fearful truism.. in my opinion Sean is great towards the chronological beginning of his stint as Indy, London, Verdun, the Somme, the Mata Hari Affair, Oganga, amazing amazing stuff, my most fervent wish is that after the war we had seen an altered Indy.. winds of change almost teases at a change in the man, mystery of the blues seems to confirm it, but then Hollywood follies, hes as naive and daffy as ever, scared of the cowboys in that saloon, seeming to take in wyatt earps commentary on shooting with a face that you could hardly believe ever saw death, let alone probably has already killed more men then Earp ever cocked a rifle at... maybe the change would have worked if he'd been assured of the shows future, but as the actor playing Indy, it was primarily up to him to make us believe that.
For my money I think Sean was cast, like George cast Anakin Skywalker, and Luke before him, because he has a sense of wide eyed naiveté, and he does, we can feel what its like, through him, to live through the early 20th century, unforunately, whenever Sean tries to look cool, tries to be hard bitten and world weary, i.e. working in Petrograd, helping sixtus and xavier, he just seems to be faking it. Its all in the eyes, and from reading interviews with sean taken at the time of filming, I don't think he had it in him to understand Indiana Jones, why knowledge is so important to the man, how a knowledge of history can lend a cynicism about the present, because you've seen it a thousand times before. Sean is great at Young Indy, but a knowledgeable, worldly wise, cynic? No. I don't think so.