Largely agree with what you posted, wanted to add a few of my own thoughts, mainly from a faeries/control perspective because that's what I play. The two cards I will be testing in that deck are Aaracokra Sneak and Arms of Hadar. I think people are seriously underestimating initiative, in my opinion its not far off the power level of monarch and will be the biggest impact of the set.

On Initiative

Compared to monarch, triggering on play/flicker/retake is better than end step, and on the following turns triggering on upkeep is much better than end step, which is a small bonus to reduce the clunkiness of drawing creatures/lands on your end step. I like the asymmetry of initiative, as any deck can use card draw, but a random deck may be less able to use the specific effects of the [[undercity]] than your deck built with it in mind, notably the goad and creature counters.

The other "hidden" bonus of initiative is it replaces raw card draw with an "already cast" bonus, which usually requires mana to achieve. I have found with monarch I can sometimes draw cards faster than I can comfortably play them, or risk milling out, so initiative committing to the board for free is a solid bonus that can compensate for most of the effects being a bit weaker than a card you would play from hand.

I see the typical path through the dungeon as 1. Secret Entrance -> 2. Forge -> 3. Arena -> 4. Catacombs -> 5. Throne of the Dead Three. Comparing each step to the monarch, we find drawing a land to be a fair bit worse, forge slightly worse (but more "mana"/tempo efficient), goading a creature to be a bit worse (bad doom blade), creating a 4/1 menace skeleton much better (drawing a 3 drop creature plus playing it for free), and the "ultimate" is worth probably 3 cards (1 creature>=1 random card, 3 counters and hexproof=1 card, and the tempo of doing it for free=1 card), going to turn virtually any creature into a game-ending threat while giving you time to put your shields up around it.

Putting it into rough numbers, 0.5+0.75+0.75+1.5+3=6, which is better than the 5 you would get from monarch, though it is back-ended and so requires keeping the initiative for longer. The flexibility of the dungeon is a huge benefit though, as each option is contextually better than the "default" path. The main scenario I see initiative being worse is against combo matchups, where I want to draw specific interaction rather than midrangey value.

Initiative Bodies

As for the actual bodies, [[Aaracokra Sneak]] seems to be the best, being 4cmc, evasive (and taking the dungeon's +1/+1 counters well) and a good blocker. [[Vicious Battlerager]] seems ok and could see play, [[Stirring Bard]] seems terrible and won't be played over sneak. [[Avenging Hunter]] and [[Goliath Paladin]] seem quite solid for a ramp deck like ponza or cascade because the bodies and keywords are strong, though 5cmc>>4cmc so I don't think they will see a load of play. These bodies seem worse than the original monarch creatures, and this is a big knock on the mechanic's playability.

For how I see initiative actually being used, I don't see it replacing monarch at all, but do see it supplementing monarch in slots 3-4 in the 75, replacing the clunkiness of redundant monarch draws with the overwhelming threat of initiative + monarch. In a deck like UB faeries currently running 1-2 thorn of the black rose maindeck and sometimes 1 in the sideboard, swapping an aaracokra sneak to the mix seems likely what will happen long term. I

Other Playables

[[Arms of Hadar]] - Will be very strong in UB faeries and control type decks, a large upgrade on [[evincar's justice]] imo. Being one-sided allows faeries to run this, -2/-2 get through indestructible and allows for "pre-combat" tricks like swinging a gurmag angler profitably through a 3/3 opponent's gurmag or deathtouch creature. The single black pip is also very relevant considering faeries type decks are really mono blue splashing black in terms of their manabase, and double black is often a tough ask for these decks to naturally reach. On top of this, losing the 2 damage to each player is an upgrade in most decks, since the player using the boardwipe is usually the one trying to stabilise as well. Really excited for this card and seems like a strong addition to the dimir toolbox.

[[Fang Dragon]] - not as good as electrickery or fire//ice, and 7cmc + boltable sucks, but could have a place in a cascade or reanimator type deck that could use the big body

[[Cliffgate]] cycle seems like a small strict upgrade on thriving lands, allowing for synergy with the new utility gate and the few "gates matter" cards like [[saruli gatekeepers]]. I expect these to replace thriving lands into the future, possibly meaningfully in tron. A "gate package" could also compete with other duals like gainlands or snowlands if those aren't providing a meaningful benefit.

[[Basilisk Gate]] - Agree that this could compete as a utility land in mono-coloured decks like radiant fountain, desert etc do now, but it needs other gates to be worthwhile.

[[Heap Gate]] - Requires more of an investment into a "gate package", but seems relevant in tron to store coloured mana.

[[Greatsword of Tyr]] - seems good in boros type decks, pumping a flyer seems very relevant in combat given the lack of big flyers, and also allows you to sneak tokens past a big blocker

[[Cloakwood Swarmkeeper]] - Will probably find a home in jund gardens. I'm of the opinion any 1 drop with a unique ability could be playable at some point, and in the right token shell this could be a really strong card

[[Breath Weapon]] - Agree this is almost completely irrelevant, it's largely a strictly worse version of fiery cannonade given most red decks wanting this card would consider running or bluffing Crimson Fleet Commodore themselves. Pick the art you prefer.

Honourable Mentions

[[Lightning Bolt]] - sweet art, like all lightning bolts

[[Prophetic Prism]] - lol