So there's a couple of things to break down.

>Anyway, I always heard that one of the reasons why swords are so iconic in pop culture is the fact that they were really expensive to produce

This one is simplistic and not particularly good critical thinking. Swords are iconic in certain cultures because those certain cultures have a fixation or interest in them. Remember, basically all cultures with decent metalworking good and did make swords (and even some without...) but it's only really the Japanese and central/western Europeans who really get into their swords. . . Despite the fact that neither sword is definitively the hardest to make nor the best.

As for them being expensive, also not really true. It's what sword and when.

Yes, Henry VIII could have swords that were worth the price of a ship or a castle... but that is because it's an item of jewellery or a status symbol just like a crown or sceptre at that point. Annnd at the same time, and earlier, we know an archer or spearman could buy a sword for the equivalent of a handful of pocket change.

Particularly the Romans though did utilise huge amounts of proto-industry, and there have been people who said resource utilisation in Europe didn't reach the same heights until the industrial revolution. That is to say, they mined and processed iron on mass and among other things made weapons out of it too.

>and tended to be more useful as backup weapons, specially in the middle ages

This is true, swords were rarely the chief weapon of the soldier. Pikes (or at least spears) and bows are often the old faithful options because they're generally better.

>That's probably one of the reasons the weapon became so associated with the archetype of the noble knight, which helped it become so iconic.

Ehhhhh.

There were plenty of cheap long blades like German (not that it was Germany at the time...) messers and such that were often used.

Again, I'd be less inclined to look for economic explanations for social trends like this.

To be clear, I'm not saying swords weren't and couldn't be expensive - they could be, but by the time of chivalric style knights in full harness they certainly weren't inaccessible.

> I understand that, in the time of the Roman Empire, swords would be much more useful as a main weapon, because armor wasn't so advanced,

Extremely debatable reasoning here.

In a fight whether, is one-on-one, or 100 on 100, pole arms are generally better... to say nothing of you know, being able to shoot people if they're unarmoured. Which makes sense and the Roman's knew that, thus their love of the javelin and darts.

>because armor wasn't so advanced

This is, itself, also debatable. There's several swords of functional armour in the period and the Romans fought them all.

>but that doesn't explain how did they manage to outfit most of their soldiers with gladii. I mean, they're still swords, they still require a lot of material and a lot more work to be made than, say, a spear, which is already an amazing weapon.

To the core of your question - they mass produced them because it was an important goal of their culture. It would be like asking how relatively uncivilised people like the Mongols and other Turkic people managed to maintain such large herds of expensive horses, or bows. Or Age of Sail empires could field such huge numbers of huge and extensive ships.

Of course we do also come back to the immense capacity of the Romans to organise and use resources as well.... but that is more a side point really.