You are right to be not completely convinced that a wide-angle zoom is a must for landscapes. "Landscape" can mean many things, from sweeping vistas to a tight composition of a distant building.
Before you throw down the substantial money for a 10-22mm or a similar ultra-wide zoom, consider this: Engaging ultra-wide-angle photography is pretty difficult:
- It's tricky to find appropriate subjects
- You need to think very carefully about foreground, middle ground, and background (specifically, you need all three of those)
- You can't as easily throw a distracting background out of focus
- Spatial arrangements and depth can get very distorted (which might be what you want)
- Small camera movements result in major shifts in convergence and perspective
- You have to pay more attention to the extremes of your frame so that unwanted elements don't sneak into the image (get ready to take a lot of accidental pictures of your feet)
The images can be very rewarding, but it takes practice. For an overview on how to use ultra-wides, this article is a pretty good start.
I suggest sticking with your 18-55 for now. Maybe practice using it only at 18mm or 20(ish)mm as an exercise. If you do that for a while and you find yourself wanting to get even closer to your subjects and wanting to exaggerate depth (foreground-background) more than you can at 18mm, then consider going wider. But only then.
Also, I know the 18-55 isn't a great lens, but it's not a bad one either. If it's not reasonably sharp at f/8 on a tripod, something else is probably wrong. Off the top of my head: Is your tripod sturdy? Can you weigh it down more? Is everything locked-down tight? Are you using a cable release instead of tripping the shutter yourself? If not that, can you set the self-timer for a few seconds? Are you sure you're nailing focus? Your depth of field is substantial, but certainly not infinite.