Why two rings?
Gameplay, balance, and clutter reduction.
Most of the abilities for a hero should come from their stats, not from magic items.
You shouldn't just be able to boost a hero to endless heights by weighing them down with basic level magic items. If you want a bigger boost, you should have to research a magic tech that lets you get a superior item.
Otherwise, all you ever need is 1-2 basic magic techs, and you can get all the magic items you need.
Where is the incentive for pursuing powerful artifacts, if I can just get the same effect by stacking up minor ones?
Its also more interesting to think about what kinds of stat boosts I want from magic items if I only have a few limited slots, rather than if I can just wear everything I can afford. Make me think about which magic items I'm going to use, rather than just using "all of them".
There's also much more of a balance risk if some item happens to be too powerful; suppose I get a bow, and then just stack up on ridiculous numbers of attack and combat speed items, which together let me assassinate your entire army on the first turn of combat.
Plus, the item UI is already messy enough (only displaying half a dozen items at a time, having to manually scroll through this tiny screen to be able to select/equip items). Letting heroes have 15+ items would lead to horrible clutter.
* * *
Basically, think of all the reasons that Dungeons & Dragons has, since forever, prevented you from having more than two rings at once. They all still apply.