Maybe it would be worth saying aloud what your ideas about the bridge skill scales are.
We have the Novice - Beginner - Intermediate - Advanced - Expert - World Class style on BBO.
Here it is shrunk to beg+ind - adv+exp.
What should be the learning curve of bridge?
My perception is and always was:
Novice: a few weeks into the game. The concepts of tricks, bidding, play and scoring covered
Beginner: first 6-12 months (assuming 1-2 evenings a week). Begins with a largely natural bidding system, Stayman, Transfers and Blackwood being high-tech tools. Unless he started with a good book, uses Blackwood with a void

. Unless he memorized his bidding system, he is quite often unsure whether a particular non-jump bid would be forcing or not. 8-ever and 9-never are the core rules of his play.
Intermediate: Learns that bidding is not about points, but about tricks. Moves to a little more sophisticated bidding system - two-suited overcalls, inverted minors, conventional major raises. Discovers that there are sometimes better ways to the contract than a simple finesse. Starts hating opponents for leading trumps as he likes crossruffs. May occasionally realize a squeeze, but hardly KNOW it

This phase IMHO lasts 1-2 years. Learns LOTT slowly.
Advanced - Feels at home within his bidding system, adds a few gadgets to it. Elimination and endplay become his daily bread. He sees opportunities for dummy reversals, really understands LOTT, can reach most of slams safely. Reads narrow-subject books - and I think that this is the right time to start learning squeezes. Advanced bridge can last for the rest of your life (I doubt I will ever feel like an expert player...)
I would agree with Roland that to move to a higher stage, you should have "mastered" the stage below - and, things I imagine to be intermediate bridge are, for me at least, far below squeezes in complexity.
Another way to look at it. How would you expect "intermediate player" to fare in tourneys? I would expect him to regularly defeat beginners, be on par with intermediates and occasionally finish above 55%.
Another way to look at it. Go to your bridge club on a good day, when the field lacks total beginners and the top experts. Try to mentally rate the players you see and know to play "serious" bridge for a few years - and ask yourself, if the intermeidate ones are skilled enough at counting hands to be able to visualize and execute a squeeze. I don't think that you will think "oh, this one could do it" unless you at the same time think "he's a good player, certainly advanced..."
And, third way to look at it: If you think squeezes are intermediate bridge, can you name enough topics for advanced and expert to warrant two more categories?
I don't think so. For me, squeezes are advanced bridge (and closer to expert than to intermediate)