Well actually there was an ancient canal, but it didn't follow the route of the modern canal. From an article on the Suez Canal:
"The idea of a canal linking the Mediterranean to the Red Sea dates back to ancient times. Unlike the modern Canal, earlier ones linked the Red Sea to the Nile, therefore forcing the ships to sail along the River on their journey from Europe to India. It has been suggested that the first Canal was dug during the reign of Tuthmosis III, although more solid evidence credits the Pharaoh Necho (Sixth Century BC) for the attempt. During the Persian invasion of Egypt, King Darius I ordered the Canal completed. The Red Sea Canal, consisted of two parts: the first linking the Gulf of Suez to the Great Bitter Lake, and the second connecting the Lake to one of the Nile branches in the Delta. The canal remained in good condition during the Ptolemaic era, but fell into disrepair afterwards. It was re-dug during the rule of the Roman Emperor Trajan, and later the Arab ruler Amr Ibn-Al-Aas."
So there was a canal that connected the Red Sea to the Nile instead of the Med. This makes sense if you are concerned about increasing trade between Egypt and the orient, but it doesn't do much for trade between Europe and Asia. If Europe lies outside your realm, there isn't much incentive for a canal along the modern route. Also, the Nile branch waterway tends to carry a great deal of silt, requiring continuous and expensive dredging of the canal and/or its periodic abandonment.
However, this begs the question as to why the Romans didn't attempt to dig a canal reaching the Med. The economic advantages to the empire as a whole should have been obvious. There may still be a problem with beach sand migration clogging the outlet, but this can be handled by rubble/rock jetties. A typical first century merchantman had a capacity of 100 to 150 tons, a length of 100 feet, a hull of 25 feet and a draft of 10 feet ("Warfleets of Antiquity" by R.B. Nelson). A canal with double the depth required for the ship's draft and double the width needed for two way shipping traffic would be 20 feet deep and have a bottom width of 100 feet. Assuming a 4 horizontal to 1 vertical side slope from the bottom to the surface (soil is assumed to be sands and silty sands), the top width would be 260 feet. The trapezoidal cross section for the channel would have an area of 3,600 square feet. The current canal route is approximately 122 miles (644,000 feet).
Assuming relatively flat terrain, the Romans would have to move 2,318,400,000 cubic feet (85,900,000 cubic yards) of dirt. This is an earth works project similar is scope (assuming I didn't make a bone-headed math mistake) to Hadrians Wall, and is much easier to build as digging a ditch is simpler and cheaper than building a masonry structure. It is certainly dwarfed by the Chinese Grand Canal and the Great Wall.
Though I don't have my crew productivity manual handy, which would give me the production rates for hand digging with pick and shovel, this seems like a job that would keep a legion busy for a few years to a decade. This would be in keeping with Roman army SOP which kept the legions busy during peace time building roads and aqueducts. The project is doable and economically beneficial.
So why no ancient Suez Canal?
One could look at the first American account of the Suez Canal to be published. By Page 406 the narrative goes into:
The Timsah cutting extends for perhaps half a mile, and then the desert is scarcely above the level of the water, and in fact in many places it is below it, so that the water covers many hundreds of acres, and the course of the canal is buoyed out sometimes for nearly a mile. As we left the hills of Timsah the wind struck us sharply, and ever and anon a quantity of the light sand of the desert would be caught up by it and sent whirling into the water; and looking closely, we could see where it had drifted little capes and promontories into the canal. Let us repeat what our captain said upon this subject, being asked:
"Yes, monsieur, this drifting in of the sand certainly seems to be one of our greatest difficulties, for the wind blows across the canal all the year round - six months one way, six months back. One ounce of sand per square yard amounts to five hundred tons for the whole canal. If it came in at that rate, it would be a long time before the company would pay any dividend. But we do not intend to let it come in; and this is how we prevent it. This sand only extends to the depth from nine to twelve feet: below this is a stratum of blue mud, mixed with a sort of clay, in which, by the way, we find great quantities of beautiful shells and fossil fish. Well, then, do you see those two huge engines which we are approaching - one an hydraulic dredger in the middle of the canal, the other an iron shute (it looked like the walking-beam of an immense steamer), near the edge? Do you see how the vast masses of sand, mud and water come up from the dredger, are poured out into the "shute," and thence on the ground sixty or eighty feet from the edge of the canal? Do you see how quickly the great heaps rise, and how they extend, almost without a break, all along? Well, monsieur, you would find these heaps almost immediately baked hard by the sun, and as they are firm enough to bear the railroad which we intend putting upon them the better to expedite the mails from India, so we hope they will be high enough to keep out the sand-drifts from the canal."
One would imagine that canals built off existing river systems were largely cut through previously eroded rock, and didn't have to contend with sand dunes. From what I typed out, it looks like the French had to come up with a modern way to build clay banks around the canal to keep it from just getting filled in.
Right after the portion i typed - the Frenchman tells the author about a hard layer of stone that required explosives to cut through. Doesn't quite sound like something an ancient bronze-age civilization could have contended with even if gifted with unlimited manpower to dig up all that clay and build walls against the desert sand. (Oops, you referred to the Romans. Makes you wonder if the Romans could have gotten through that rock)
The Nile is a very easily navigable river because the wind mostly blows upstream and you can simply lower the sail to go downstream. It is deep enough for ancient ships to navigate, so you're going to look for the optimal place to dig your canal, which was not Suez. You are going to connect the shortest distance between places your ships can reach, so the shortest distance between the navigable Nile and the Red Sea with a stretch in between where you can dig a canal relatively easily. That is why it was dug where it was.
Nowadays with bigger ships the closest two places ships can reach are the Med and the Red Sea, so it makes sense to dig it where it is now.
The history of this ancient Suez canal is disputed by historians. There is archeological evidence there was in fact a canal in the 6th century BC. But if it was completed it would have brought economic disaster. The Great Bitter Lake was important for farming, but this would have been made impossible by influx of salt water from the Red Sea. So the Pharaoh's discontinued the canal.
It was re-dug during the rule of the Roman Emperor Trajan
I think you answer your own question a bit here. THIS was the ancient Suez canal. Only, it didn't go straight to the Mediterranean, but to the Nile delta, from which you could continue on into The Med
So there was a canal that connected the Red Sea to the Nile
instead ofand the Med.
This makes sense if you are concerned about increasing trade between Egypt and the orient, but it doesn't do much for trade between Europe and Asia. If Europe lies outside your realm, there isn't much incentive for a canal along the modern route.
Egypt has been connected to Asia and Europe pretty much since forever. Which makes Asia and Europe very interconnected, not only throughout Egypt but also through Anatolian, Black Sea & Levant Trade routes.
There was no need for a direct channel since long distance trade (as we are used to now) barely existed back then. Most trade was just coastal town to town, so for example silk from china could have been in the hands on a dozen traders before it ended up in Egypt, to be from there taken by an additional dozen traders into the Mediterranean, into Europe.