Theoretically, you can adjust the height of a threadless headset moving around the position of the spacers. The problem is that most threadless headsets come with very little room (or none at all) to adjust the stem up and down. The leaves the only way to adjust the height is by purchasing a new stem, which doesn't give you the option of switching mid ride.
Also worth pointing out that while the connection on a threaded headset may be stronger, the threadless setup is strong enough for most riding conditions. Threadless headsets are used on all kinds of bikes, from road, to mountain, and even downhill. If it didn't provide a strong enough connection, you wouldn't have manufacturers risking lawsuits with something that is known to be inferior.
Also, a threaded headset has a single point of failure that's difficult to inspect. If you are using the style of quill with an expander (see below) there is a decent chance that over time the stem will break from the pressure of the expansion (I know someone it happened to, twice). With a wedge style, this not a possibility, but you still have a single point of failure if wedge nut or bolt brakes, or even if it loosens over time. There's always 2 bolts on threadless, so no single point of failure, and it's easier to inspect what's going on to see early signs of wear.
The biggest problem I know of with threaded headsets though is that the stem has a tendency to rust to the steerer, and is sometimes practically impossible to remove. This is preventable with regular maintenance, but there's a lot of bikes out there that don't get as much maintenance as they need, and most non-enthusiasts would probably never think of checking the quill for rust and regreasing a couple times a year. Most people would probably be afraid to disassemble the headset to ensure things aren't starting to rust, and many people don't like going to the bike shop for things until something actually isn't working because of high prices.