There was a chance we would. Stanley Kubrick and Arthur C. Clarke, over the course of the four years they spent creating the story, considered having an alien character interact with the man-apes on prehistoric Earth: Clarke wrote a draft of the novel with one. Carl Sagan said that Kubrick and Clarke asked his opinion on depicting aliens; Sagan said that would be a bad idea, because the aliens you're imagining would likely have evolved so differently from us that we might not even recognize them as living creatures.. (Notice that neither his novel nor the film Contact ever show an alien.) The slit-screen effects used to create the Stargate in the sequence "Jupiter and Beyond the Infinite" were also used in tests to create patterns that might look like aliens; this was nixed. In the last year of production, as another test, Kubrick had dancer Douglas Richter move and contort in a dot-covered suit in front of a dot-filled backdrop, thinking that maybe the footage could be manipulated to look like something alien and alive, but it looked ridiculous.
So. No aliens on-screen in that movie. Except for fellow geeks I've known who apparently know the film better than Kubrick and Clarke did.
Years ago, I mentioned online that I'd had a dream involving 2001 where my dream-self had been told There's an alien in it if you know where to look. My dream-self saw one, but clearly a fake, pictured on a monitor on the space station. My dream-self was disappointed. I mentioned the dream, and someone replied There are aliens you see, though. Really. Here.
He pointed out that shot, from the Stargate sequence. The shapes in the upper half of the shot? Aliens.
Except no. THE PEOPLE WHO CREATED THE FRICKIN' FILM SAID "no aliens." (That's in lower case because they almost certainly didn't yell.) They said so repeatedly, in many venues, whenever it came up. But considering that people think Kubrick faked the moon landings, a conspiracy that only works if something like one million Americans were in on it and never ever spilled the beans, Kubrick and Clarke's word wouldn't be good enough, right?
How often are we completely certain we are right when we're wrong? My fellow geeks can be really, really bad about that. (I'm focusing on geeks at the moment because I've had plenty of experience as one.) People: AMBIGUITY IS OFTEN NOT A BAD THING. We can interpret what those shapes might be; Kubrick and Clarke didn't mind that. But, focus on the "might."
We don't need to explain everything.
We don't need to codify everything.
We don't need to be certain about everything.
It can be tempting to want to; we like Knowing Stuff. We like Having Special Knowledge ("What you DIDN'T KNOW about the Back to the Future pine trees!"). We like Pontificating. We like interpreting, and we like being right, even though "interpreting" and "being right" are separate goals. At most, they overlap a bit, Venn-like.
It's easy to convince ourselves we're right. Probably too easy.
...maybe those nonexistent aliens in 2001 know what's right.