Sorry, but this summary justification is incoherent.
Dromons have the same move speed and reach as Triremes, but they are actually better for scouting because the ability to take pot-shots for xp at remote barb camps means they get the +1 vision faster than Triremes.
A virgin Dromon can encounter (and kill) barb galleys without getting hurt at all. That requires some luck, but being unscathed is not an option at all for the well promoted Trireme. In head-to-head battles the Dromon is not taking damage on its turn, so the strength of 8 versus 10 hardly matters, especially if it gets the first shot (not hard). All told, the Dromon spends much less time healing than the Trireme. Personally, I have no trouble getting range+logistics on Dromons, but it is quite rare for me to get even a third promotion on Triremes.
That said, waiting for Frigates to come online is painful. Even Galleasses with range+logistics are useless...
I wouldn't call them useless. You can start taking capitals with Dromons & one melee unit on Deity early, and clear the map with Galleas before you even tech Frigates. I've done it, and it works, but it only works well on water maps.
Actually, it can even work on Pangaea if you get lucky with capital placement. There was a Deity gauntlet a while back where I tried clearing a Pangaea using mostly dromons. It requires some map luck but it works.
Basically the strategy is, immediately DoW a neighbor CS to earn promotions for the dromon, (plant an expo next to it if you don't start close to one, because you need to be healing in your borders)
If you didn't plant an expo, considering capturing that CS early to ensure you have two adjacent coastal cities.
Most pangaeas are ice-locked in at least one place on the south and north pole. So you need one small land army to capture a city on the other side of the ice. The strategy falls apart if you're completely ice-locked (IE at the pole) or have no neighbors on your side of the Pangaea. (And can't take at least 2 coastal capitals with your original dromons)
I used a scout, warrior and one worker to lure enemy units out of the city into dromon attack range. This ensures that your dromons can attack the city without getting killed. If there is an archer in a city it will ignore your melee (even at 95 health) and focus fire on the dromon.
After clearing a couple cities, you need to wait until Compass, because around t70 the AI cities can one-shot dromons. But, this coincidentally gives you time to send your CB army to capture a city on the other side of the polar ice and start building dromons there as well. Then, when you hit compass, boom you have range/logistics galleas, which, FYI, are totally badass. You can then finish the map with Galleas, using your CB army to tackle remaining inland capitals. If that stalls out, finish at Navigation around t150.
EDIT: To be clear, what makes dromon bad-ass is the ability to *upgrade them into galleas, which no one else can do*... The difference between teching compass on T90 with Byzantium and any other civ is about
6-8 extra galleas on t90.
Yes, this is somewhat artificial, because it requires at least 4 AI coastal capitals for it to work well, not a likely thing on Pangaea, but... in an archipelago domination game? Well, in that case, Byzantium just flat out RULES. Honestly, I'd put them in the top 5 for fast archipelago wins. Not easiest, but fastest. They might even be #1. Considering it's the ONLY ranged vessel in the ancient (or classical) era, well, that says it all. I'd probably put Denmark, Attila, Polynesia and Dido higher for "ease of early war victory", and Suleiman is fighting for a spot in that top 5 too, but man, nothing chews through an archipelago like a fleet of promoted dromon... (Half promoted to double-tap, half promoted to range, because usually there aren't enough firing positions for the whole fleet to attack from within 2 tiles of the city)
Arguably Denmark is better because CBs can come in from out of range and fire from rough terrain in one turn. Arguably Attila is better if there's enough land around the city, but that varies by map. However, once you manage to build or capture GLH, open Exploration, and your recently upgraded Galleas have logistics.. at that point they're unbeatable. Which you should be able to achieve by t100 in most games. (even t85 compass if you burn a liberty GS)
(Re: That Gauntlet - I ended up not submitting that game because it wasn't going to win best time)