The Grand Canal of China was closer to a road system than a modern canal as far as game implementation goes (it was in-land, was for quicker transportation, and connected rivers, which, in civ terms, we can't navigate). However, that's not the point about whether there should be modern canals.
In previous games, I found it very easy to work around this by just building a city on a one tile gap between land and water. However, there are two things in Civ5 that make this more difficult. First, the switch from squares to hexes makes the number of times with a one tile gap much smaller. A lot of the time, it seems to be a two tile gap. Second, the minimum distances between cities means you can't string cities through in-land lakes to reach the other ocean.
That being said, what I don't want to see is something like a 5+ tile canal connecting distant landmasses. Canals connecting oceans have historically been on very narrow isthmuses (the equivalent of one tile connection), in which case a city would be sufficient.
I think the fair compromise is this. Allow canals to be built on grassland when there is no more than a two space gap between oceans (for these purposes allow lakes to count too). Make them expensive and don't let them get built until an industrial era tech (to represent modern canals like the Suez and Panama).
ETA: To address the logistics. I would say this. Any ship in a canal would become automatically very vulnerable to ground units (and, obviously, they could be attacked). Also, any ground unit can essentially "shut down" the canal, i.e., block ships from even passing them if the two sides are belligerents.