> I doubt it has close resemblance with medieval long sword fighting, though :-)
It does actually resemble it very much, but medieval longsword fighting was probably very different than what you think it was.
> It must have been a lot slower fighting in leather, chainmail or plate armor than in this ultra light modern equipment.
Not really. The main difference is visibility. First, the modern HEMA equipment is a lot heavier than e.g. standard fencing gear. It's a lot thicker (like those dog attack suits) and often have steel or kevlar plates in the inside. Second, medieval gear wasn't all that heavy. I have a full suit of maille (as it's really called) and it weighs less than 15 kilos, helmet included. A full steel plate armour shouldn't weight more than 25 kilos. That's less than modern soldiers have to carry around on the battlefield.
The biggest difference is that a fencing mask gives you better visibility than a historical closed helmet.
> these guys fight one on one
That's what happened in medieval times too most often. The original medieval books were written mostly for one-on-one combat, either for dueling or trial-by-sword. That happened a lot more than being caught in a war on a battlefield. Swords have little use on a medieval battlefield anyway. You use different weapons and tactics.
> And fighting on some uneven, damp meadow [...] would be hard compared to fighting indoor on a floor.
My HEMA group trains for this as well, and I suspect many other groups too. It is also mentioned in the medieval books. I have trained in loose sand, in the surf on a beach, in deep snow, etc. It's true that competitions are usually held indoors on an even ground though.