Mines aren't the most important, alloys are. Of course, minerals are also very important by extension because alloys are produced with minerals, but an empire with 1,500 alloy production and only 100 mineral production should be expected to easily beat an empire with 1,000 alloy production and 2,000 mineral production, all else being equal, presuming that the latter empire cannot shift his minerals to alloys fast enough.
Anywho, Ecumenopolises, even small ones, are way more efficient than regular planets at creating alloys. Ecumenopolises can actually save you minerals, unless you're converting a mineral-rich planet, which you obviously shouldn't do.
- Ecumenopolises have a +20% bonus to production inherent to them, which means more alloys per pop
- Ecumenopolis Civillian goods and alloy districts give 10 jobs for only -5 energy, whereas upgraded building variants require a building slot and -2 rare resources, plus other things.
- Ecumenopolises have 100% habitability by default. By default, "ideal climate" planets have 80% habitability, close matches 60% habitability, and mismatches 20% habitability.
Okay, so what's that all mean in the greater picture, and how's that saving minerals?
- The increased production bonus means you can use less pops to get the same target alloy or consumer goods production, which means you're using less pops. Since pops need consumer goods, that means you need less of those, which means you need less minerals to make those.
- The favorable upkeep on Ecumenopolis districts means that even once the teams of conventional planets manages to match the output of a single Ecumenopolis, they'll need a load of upgraded T3 C-Goods and Alloy buildings, which will require a lot of rare resources which will need to either be bought or synthetically produced, and in the case of synthetic production that requires jobs and a very non-trivial amount of mineral input (-10 minerals per synthetic production job to create +2 rare resources at base). So you're using even more minerals just to keep your regular alloy foundries running, whereas the Ecumenopolis takes those mineral inputs into alloy outputs far more efficiently.
- Every -1% habitability is a +1% increase in a pop's consumer goods consumption, amenities consumption, and food consumption. This means that, even if you could match the mineral output of an Ecumenopolis with the same amount of pops sprawled across different conventional planets, they'd still cost more to upkeep than the Ecumenopolis pops. This means you have to divert more pops to consumer goods production (or trade with the proper policy), local amenity production to stay above negative, and food (not really an issue but it's still useful for that local planetary growth modifier decision). So really, you're still using more pops to get the same result.
In practice you're never going to say "Oh I hit my target alloy production, I guess I'll just stop developing my Ecumenopolis," so instead of just producing the same output for less, in reality you're going to be consuming roughly the same materials for a far greater output.
So what's the hubbub on the Ecumenopolis? Well, they simply make more from less.