Logistically, it makes little difference if ship 1 takes people or lots of different goods to Port A, it gets hauled or railroaded overland to Port B and put on a different ship. It's only when bulk carriers are considered, and the transit of major capital ships that it really matters, and this is also tied in with when sea transit becomes a lot swifter - i.e. taking several days to transfer is nothing if the total journey is a couple of months, but when it can be cut down to a couple of weeks then adding on several days suddenly becomes uneconomical.
Transshipping is not nearly as easy or convenient as you make it sound, especially before containerization and/or railroads. A ship must be unloaded by hand, its goods repacked onto mules or whatever (even if some of the trip is on rafts, you'll need mules at some point to cross the Continental Divide) - and a lot of them, as each mule carries <100kg, and even a clipper ship, where speed is most important and carrying relatively little cargo, carried ~1000-2000 tons = 10,000-20,000 mule-loads. And then repacking them on the other side. The route 'round Cape Horn is about 7,000 nautical miles = 24 days at 12 knots (not an unreasonable speed for a cargo ship in the broad period from 1700-1900) - and a clipper ship could take it in half the time. If it takes, say, 3 days on either end to load and unload the ship, and 6 days for the mule train, it no longer makes sense for clippers, and makes questionable sense for others - especially once you take into account the cost of loading, unloading, and guiding the train (plus, presumably bandits!).
A canal also allows the swift movement of warships - that's why the US was interested in it, by the way: before Panama, the Atlantic and Pacific Fleets were basically completely independent because it would take over a month for either to reach the other.
EDIT: By the way, in the modern day transshipping makes much more sense. Railroads and containerization probably reduce the time to about 1-2 days, which is actually competitive with transiting the Panama Canal (10 hours to transit, plus time navigating in and out, and waiting your turn). But you'd need two giant container ports and a big-ass railway (though I like the idea of the railway basically operating in a continuous loop