It's not just about population - China by the 1800s had a population approaching half a billion, but they had almost no industrialization compare to the Europeans at the time.

>Were they really there? I thought they made it to the point of being equivalent to the 15th century but never got any further technologically.

In terms of metallurgical technology, they were closer to 13th century Europe-level. Just looking at iron production, the Romans of the late Empire were still running dinky bloomery furnaces to smelt iron- not much different from the ones their forefathers were operating when their city was found.

Historic and archeological evidence suggest the Romans never produced more than a hundred pounds of iron from their furnaces, while European smelters by the time of the 1200s were already producing nearly a ton of iron per run from their larger furnaces (which were more efficient in terms of manpower and fuel consumption). By the 1300s, they were able to produce a few tons of iron from each furnace operation, which spelled out to a greater and cheap iron supply that helped pushed the adoption of plate armour, and then gun artillery.

I think plagues and wars continually came around keeping the population down. As well as loss of their best arable lands. By the time the eastern roman empire was the only part left much of western europe had become much more productive and their populations were able to grow bigger.

Also i think your last point is a big factor. While rome was wealthy throughout its times the increase of wealth to the powerful western states by their access to the americas was massive. Constantinople finally fell in 1453. Columbus did his thing in 1492. Sadly rome never knew that the americas existed.

Au contraire, they made it to the Americas twice that we're aware of, although there's no record of Romans returning from the new world. The ships that were found were most likely blown across the Atlantic by storm.