So I finally took the time to look stuff up, and watch some videos on YouTube. And it turned out that I simply hadn't understood enchantments at all. You can put various elemental enchantment on gear, like an enchantment that gives "+15 fire". When I tried that on a random hero, the effect was minor, so I dismissed that part of the game and didn't bother with it. Boy, was I wrong! What I hadn't seen when I was doing that was that every hero has his own preferred element. Put "+15 fire" on a hero whose preferred element is nature, and not much happens. Put it on a hero whose preferred element is fire, and the combined score of all fire enchantments on that hero determines the level of his skills. And higher level skills have a huge effect on the power of heroes.

Before I learned this, my best hero had a power score of 14k. Now that I enchanted all my heroes with their respective elements to the max, my best hero has a power score of 32k. And pretty much every hero doubled his power, so my weakest heroes are now where my strongest hero used to be. The effect is bigger on heroes that have more skills, so suddenly ditching the old classes of heroes and replacing them with heroes of classes you unlock later makes sense. I haven't fully gone down the hero optimization rabbit hole yet, you can find a lot of guides and spreadsheet simulators for that online. But I rerolled some skills that didn't improve the main stats of my heroes, and that boosted their power further. Right now I am pretty happy with the result, and will slowly replace the less good heroes by the more advanced classes.