If it is an "iconic" design - something that creates a type or genre of firearm, it can be a classic. However, it takes time to make that happen. And as time goes by, the discerning purchaser of firearms is presented with newer models than what another generation thinks is the limit.
To the point, we've mentioned everything around it, but why not the S&W auto pistols starting with those in the 1950s to now?
First, it was designed on a classic, the P38, in response to a Army solicitation for a 9mm pistol to replace the 1911 - in 1954. (That vs. thing started a long time ago.) It was marketed, not shelved, and was about the only American DA/SA available for a long time.
When it showed promise, the double stack version was introduced and sales took off. We then went thru a significant upgrade with the 2d generation, into the 3rd, and they were seen on the belts of cops from coast to coast. They made it into the movies and are still depicted in TV series as the weapon of choice for characters.
Smith still makes them for large purchasers to order, and overruns are slipped into the market NIB to this day. They are a common item in pistol competition, too, with models using 9mm, .40, 10mm, and .45ACP. Smith made an improved model labeled the TSW which has a better trigger, enhanced rails, and came with Novak night sights, and as that line progressed, added the Dawson Weaver rail as standard. Same supplier as the one made for 1911's that don't come milled for one.
Classic? Over 62 years of production and still in service, with LEO trade ins on the market right now. Originally blued steel with wood grips, then the most favorite models came all stainless with the factory polymer or Pachmayrs. Its gone from old school production to the modern level factory, from roll marked to laser etched, and has models with 5", 4 1/4", 4", 3 1/2" and shorter barrels, with full capacity to pocket carry capacity. Forged to MIM parts, plain jane to presentation grade, service carry to Chief's Specials.
We very well could have been carrying them into Vietnam if the typical cost cutting and low prioritization of the 1911 hadn't happened. As it is - they were, with the Navy silenced "hush puppy" variant.
Does the shooting public consider it a classic? Using most of the definitions provided, it would seem a slam dunk. But I will suggest it's not - because the public, however informed it may be on them, won't offer that opinion.
Observe the pricing on them in auctions, the few articles written about them, the rare post in forums. There aren't crowds of people bidding them up yet either. The public holds them in less repute than the HK P7 - another classic.
The S&W's are still too new and underappreciated. Some sell for as much as the P7, but the overall market is depressed.
The public says what is or isn't a classic, and they vote with their dollars. The keen eyed collector, however, observes the masses and then does the opposite.