There are a few other points to make when you’re looking at the long-term impact of a card. As you put it, EDH looks for very different things in a card than tournament-played constructed formats. You discount the mana cost dramatically when you’re looking at EDH and focus instead on the effect. That’s why you like Tyrant so much; it’s expensive, but you get a huge beatstick AND an ability to disrupt artifact strategies AND a alternative win condition all in one card. The effect is enormous. Similarly, Hydra Broodmaster is too expensive for actual constructed play, but it, too, is a big beatstick AND the effect you get out of it if you pump tons of mana into it in constructed is game-ending.

Some other critical questions to ask about cards for long-term demand include:

1. Does it die to removal? (All else being equal, a creature that gives you a benefit even if it eats a cheap removal spell after being cast is better.) Lifeblood Hydra passes this test with flying colors, making it very appealing for EDH. Stormbreath gives you a much smaller impact (maybe 5 damage) so it scores less points here. Some, but not tons.

2. Does it threaten to end the game on its own? Alternative win conditions or massive effects attached to creatures that are not otherwise useless (hello Tyrant) are going to have some demand.

3. Is it a combo piece? Generally, I always buy playsets of potential combo pieces in any new set. These usually include cards that have relevant activated abilities that do not require the creature to tap, an ability that untaps a creature, an ability that returns cards from the graveyard to play, abilities that allow you to cheat the mana cost on getting permanents from your hand or graveyard into play, or cards with triggered abilities where the trigger is something that it’s not hard to do infinitely in EDH. For example, Hydra Broodmaster is a win condition with infinite mana. Selhoff Occultist is a win condition with infinite LTB triggers, like you get in Sharuum. (Obviously, not all combo pieces are created equal.)

4. How well does it work with Nyxthos? I don’t think this is a trivial question. Like you, I suspect Nyxthos is a powder keg waiting to do some damage in constructed at some point. Cards that feed the Shrine and translate the Shrine into a win once it’s fed seem like they bear watching.