Photos/descriptions of the cataracts themselves would be a great help. I looked over the wikipedia for the cataracts and it looks like it looks like it wouldn't have been feasible for the Egyptians to have cleared the cataracts from the Nile. The only option would be a bypass canal linking navigable stretches above and below the cataract. Obviously this solution would depend a great deal on the geological situation at the construction site but I think the Egyptians had the ability to build the canals if they wanted to. They were able to build the Canal of the Pharaohs alright.
What we really need for this thread is a trained geologist and engineer.
EDIT: Saphroneth is geologist so he might be able to help
I'm going to PM Saphroneth later today. Hopefully he can help.
Thinking again, it becomes more obvious that they couldn't clear the river as it was flowing, so a canal seems best - Ideally replacing the Cataract entirely. However, I don't know whether the Egyptians knew how to make/use locks, so I would expect them to build a canal that doesn't need them.
Regarding why would the build them?
1) Trade and Tolls- The Kushites seem to be able to have significant populations in the area beyond the Cataracts, and clearing the Cataracts would allow greater access to each others markets.(in both directions, so why not have the Kushites give the canals a go
) They weren't insignificant, they did found the 25th Dynasty after all.
Regarding what there was to offer, we have some evidence of significant trade.
wikipedia said:
Over the centuries, trade developed. Egyptian caravans carried grain to Kush and returned to Aswan with ivory, incense, hides, and carnelian (a stone prized both as jewellery and for arrowheads) for shipment downriver.
In addition, Kush is meant to have been at the heart a vast trade network, and controls access to sub-saharan trade routes, the increased access to Egypt would benefit everyone upriver, who would in turn benefit from Egyptian grain, bronze, and other goods.
Canals would allow trade ships to carry vastly more goods than the caravans, the profits of which could be taxed at tolls at the canals (which would be relatively easy to fortify to ensure taxes could be collected).
I'll accept that there is a chance that there wouldn't be enough to pay for the canals and the forts, at first - but my instinct would be that there would be, and increased over time as the trade between both markets grew. In addition, if there are any resources around the cataract-canals that are worth exploiting, it could be enough to make the difference. After all Abu/Elephantine wasn't just the centre of the ivory trade, I vaguely recall reading about various types of stone quarries nearby, and it is at the first Cataract, and as such right next to the first Canal.
2) Expansion - If you can control the canals with forts, it makes sense that it then allows you to tap into the local resources, which may in turn lead to wars with the locals, especially Kush. I don't expect a Pharaoh seeking to have these conflicts from the get go, there may be some, but if relations turn sour and the markets are closed, the forts would allow them to force them open again.
In addition, any cities captured in such a war would mean that Egypt Proper could expand southwards with its population, with very secure waterways. At the very least, if a Pharaoh decided to conquer Kush for their resources, the canals would certainly strengthen his position.
Now I am unaware if the Pharaohs had any concept of population management - but assuming some sort of population boom due to good harvests, if we have canals extending the navigable length of the Nile, it also means there are more locations Pharaoh can establish cities for controlling valuable resources (and potentially increasing the maximum area that could be farmed in worse years, reducing the overall strain on farmlands). Assuming they have that level of foresight.
I do find the idea that iron-rich Kush and Meroe could be controlled by the iron-poor Egyptians, which could lead to a larger, iron-rich Egypt once iron tools come into play.
In addition, conquering all of Egypt would be a nightmare, you could conquer Upper and Lower Egypt, but to push to Kush/Far Egypt and Nubia would mean flat out fighting your way past fortified rivers!