Core set has stringent rules that rule out many potential dual lands. e.g.
no pain
no shuffling
no basic land types
not strictly better than basic lands
not too complex
no advantage to opponent (e.g. free creature token)
can recoup tempo loss (e.g. no bouncing)

Do you agree with these criteria? What are other criteria? And based on these criteria, what are some good designs of dual lands fit for the core set?

Discardlands (~ ETBs tapped unless you discard a card) will happen, but probably not in the core set. Basic taplands are still an option, if only because the basic set of allied-color ones is not plane-neutral. I wonder if the move to more uncommon doesn't mean there will now be duals at that rarity again?

ETB tapped Tri-lands seem promotable to rare. Might require a few more years for people to appreciate that move, though... Alara uncommons aren't really in short supply yet.

I don't see why we can't get something similar to Tainted Isle and company. Taps for colorless, or U/B if you control an Island or Swamp. Just Glacial Fortress with the etb tapped switched with colorless, I suppose.

Also, I wonder if we'll ever see "When this land enters the battlefield, search your library for a Mountain or a Forest and put it into play..." Better than Wooded Foothills because you don't pay the 1 life, but worse because you got to choose as soon as you play it. Seems kind of broken. Which only reminds me how broken those damn Foothills really are.

I'd emphasise "Simple". You want people to see them, get them, use them. Drawbacks are needed ofr obvious power-level concerns; but they shouldn't be fiddly.

The "plane neutral" requirement is an old myth that refuses to die. If it was ever true of core sets, it hasn't been for a long time, but I don't think it ever was: Adarkar Wastes was in lots of core sets, the Caves of Koilos and Yavimaya Coast are storyline locations, and so on; more recently we've had characters like Odric, Master Tactician and Krenko, Mob Boss, who are from Innistrad and Ravnica respectively but were introduced in core sets.

I'd love to see Coastal Towers with basic land types, but I don't think it'll happen for some time, because they'd be inherently overshadowed by the shocklands even though they're usually better than Guildgates.

Rare dual lands are always a tricky proposition. On the one hand, experienced players are usually rather excited to get a dual land as their rare in a booster (because they're very valuable, because they go in so many tournament decks, because good duals are mostly kept to rare, because that sells more packs for Wizards). On the other hand, new players are usually not very excited at all about dual lands, and there's not much that can be done about that. I imagine lots of kitchen-table newbies cracking Ravnica packs were even disappointed in the shocklands they opened (until they made it to a FLGS with people with trade binders). The one exception to that that occurs is the Celestial Colonnade cycle, especially notable for Creeping Tar Pit and Raging Ravine. Those were popular both with newbies and with tournament players.

I think you're a bit wrong, Alex. While Wizards has indeed been making an attempt to add some planar flavor into core sets, and had a sort of "tour of the planes" theme in M13, I'm pretty sure I read a statement from Maro somewhere stating that they try to print dual lands with neutral flavor. That way they can reprint them in whatever set they think is necessary. That's why the shocklands don't have guild-specific names, after all.

What I mean is that a complete set of simpler duals duals than be occasionally reused in expert expansions would be a valuable asset. Not many of the dual land sets qualify for that (in fact, there are so few 10-lands sets that we can expect a few of them to be completed, especially upon revisiting the planes they came from).

I remember reading, when tenth edition came out that Maro expressed regret that they were forced to use Yavimaya Coast and Caves of Koilos in the core set. That's why, when Odyessey came out, they made sure to use generic names on the rare land cycle (Mossfire Valley et al.)... which is kind of funny, since those 5 never appeared in a core set. They're due some day, I guess. Either them, or a set of lands like them that also produce colorless.

I don't think the rule so much is that Wizards won't put rare off-world lands in the core set, so much that they try to make promotable lands generic in the first place.

It looks like Mossfire Valley and friends would just be worse than Fire-Lit Thicket, generally.
Anyway, to respond to the original question: Yes, I do agree with those criteria. I think the checklands are pretty much the perfect dual lands for the core set. They're easy to understand and at a great power level.

Technically, you need to make one of those combinations of mana. Two Fire-Lit Thickets only make . But I agree. It's a better card.