True. However, we could send unmanned robot ships, loaded with biological material, to seed other worlds. They could be slow, no problem. We'd never be around to see the results anyway, but it would be relatively cheap, and some percentage of them would be successful. It might have been the way things started here, before evolution kicked in, but that would mean some earlier species pulled off the trick a few billion years ago, and perhaps that's too early in the history of the universe for such a development. Anyway, it's one way to spread out. Rather remote, of course.
A trip via wormhole would be interesting. You'd ride the space elevator from the Earth's surface up to the spaceport at its top; transfer to a spaceliner; depart earth at high speed (accelerating all the way), and sail for a few days to wherever they find the wormhole or build the Stargate (inside an asteroid? Beyond Pluto?) The wormhole/stargate itself would probably look something like a big, empty-framework rectangle or cube or ring floating in space (the stars on the "other side" of the wormhole might be seen shining through the hole in the middle!). Your ship shoots towards the wormhole, zips through the middle of the framework -- and suddenly it's in the Tau Ceti system, eleven light-years out (this happens literally in no time; travel time through a wormhole would probably be near-zero)! Your liner then flips over, decelerates to match the speed of the target earthlike planet, and ties up at the dock at the top of the Tau Ceti space elevator (built by the first expedition through the wormhole). Total transit time (passenger) would be a few days.
Interestingly, space vessels used to fly through wormholes would not necessarily need powerful engines; they needen't even be spacecraft at all! For example, a captive wormhole might be dragged to or built in an orbit around the Earth. A space elevator could then be built from the surface of Earth to the "Wormhole Station" in orbit, where the "tracks" would be extended through the wormhole itself and connected to another space elevator built on the destination planety. This would create a hard, physical connection betwem Earth and the target world that would allow "trains" of passenger and freight cars to be taken up from Earth to the Wormhole Station, through the wormhole, and down to the planet on the other side. This would be a train trip through space -- a railway to the stars. Interstellar travel could become as easy as saying "I'd like to reserve a sleeper on the 9:50 22nd Century Limited, to Procyon, please."
To a society with wormhole travel, there's no need to build starships. In such a world, '"all space travel is local".
A great deal of scientific thought exists to support the idea that wormholes can exist and could be used for interstellar travel. Making one might be difficult, but I'm guessing that there are shortcuts sprinkled all throughout space and time already -- leftovers from the creation of the Universe -- that we might find and use.