I really hope you never work at Naughty Dog.
Link serves as a pretty emotionless template that Nintendo can change time and time again. All the characters you mentioned have very definitive personalities and character traits. Rebooting it is not the way to go. How about they explain the massive mindfuck at the end of Jak III?
Here's the thing. If you make a direct follow-up to the original games, you know how much it would sell? Not much. Look at Lost Frontier. Barely anyone cared that it was coming out. The OT here on GAF was like three pages long or something. It didn't sell. Part of that can be attributed to the fact that it was released on the PSP and PS2 in 2009, but God of War: Ghost of Sparta was released a year later on the PSP and people noticed because it's a franchise that people actually still care about.
The Jak canon, as it is now, does not have enough appeal to justify a new game. The change to a futuristic gritty setting turned too many people off, and while Jak 2 and 3 weren't commercial or critical flops, they didn't have the consumer mindshare that the first one had.
However, the Jak & Daxter
name still has some potential. People remember it. Jak was going to be Sony's new Mario at the beginning of the PS2's life. People played and enjoyed the first one. The Jak name isn't guaranteed to sell, but it would get people to look at what you're offering.
But if they look over and you're saying, "Okay, it's Jak 4! You're playing as the same Jak! But you've traveled back in time and people are calling you Mar because we foreshadowed in Jak 3 that Jak was this guy who invented all the modern technology in the distant past! And--" you've already lost all but the small minority of people who are already interested in the next Jak game.
If they look over and see something that looks good, possibly something that reminds them of Jak 1, and presents the gameplay enhancements of the sequels in a way that doesn't turn them off, they'll pay more attention.
I think that there can be a Jak game that appeals to people who liked Jak 1, people who liked the sequels, and people who have never played a Jak game before.