Key to getting to 3000 hits (or any of the major rare benchmark numbers) is performance deep into the career, past the point that everyone else starts seeing significant drop offs. There are plenty of people who can put up nice numbers in their 20s, doing it in the mid to late 30s is hard. For example, Altuve is behind Elvis Andrus through their Age 28 seasons in hits, not that I think Andrus is likely to challenge to 3000 either.
Altuve is way ahead of where Biggio was through his Age 28 season, but Biggio had nearly 1100 hits from Age 35 season on.
Altuve is comparable to where both Jeter and Beltre were through their Age 28 seasons, those two had around 950 and 750 hits, respectively, from Age 35 on.
Altuve is behind ARod and Pujols were at Age 28, both them slowed production in their late 30s before getting there at 39 and 38.
Ichiro is tough to use as a comparison since he didn't make his debut til 27, but he had over 200 hits each of his first 10 seasons(!), including some monster numbers in there (262!), and broke 3000 in his Age 44 season.
Now lets compare to a few other guys who didn't get/haven't gotten there:
Dustin Pedroia - a couple hundred behind Altuve through Age 28, but still respectable (ahead of Biggio). Since then he's a had two 190+ hit seasons, but injuries have derailed him, not sure how much he has left in the tank at all. He's just over 1800 hits heading into his Age 35 season.
Michael Young - a later MLB debut than Altuve so behind him at Age 28 by a couple hundred, but put up very comparable hit numbers in his prime as Altuve (5 straight seasons of 200 or more). Didn't suffer any significant decline until his final season when he got 145 hits in 123 games. Retired after Age 36 season over 600 short of 3K.
Miguel Cabrera - About 180 hits ahead of Altuve through Age 28 season, now at 36 he needs 324 more hits and I'm not sure if he's gonna be able to limp there.
Robinson Cano - About 150 behind Altuve at Age 28 season, now at 35 he needs over 500 hits. Before his suspension this past year, he'd been remarkable consistent through his early 30s, but will now need to maintain for several more years to get there.
So comparing to all these guys, Altuve can definitely get there. But at his current pace, it'll take to his Age 37 season, longer if he ever slows down or misses meaningful time. It's tough to call that a lock. 3000 hits is really hard.