I wouldn't say there's "no way" to combine these things without the kettlebell. But I would say the kettlebell is ideal for it.
The off-centered handle design is key to the kettlebell's versatility. Grabbing the center of mass in a dumbbell means you're grabbing exactly the weight of the dumbbell no matter what movement you're doing. The off-center handle of the KB makes it feel heavier than it actually is. The off-center handle also makes mobility work more demanding because the load is, by design, unstable. Hold a 35# dumbbell overhead and then a 16k kettlebell and see for yourself. For some movements, like the swing, this design makes little difference, but others like the press, get-up, snatch, bent press, windmill, etc, where stabilizing the load is part of the movement, the design is integral.
The versatility is what I think most of us mean with that statement. You can do a lot more variety of movements with a kettlebell than a dumbbell or barbell. (
@Pavel Macek will undoubtedly chime in here on the dumbbell because he has researched methods of moving the dumbbell most of us haven't.) And compared to Olympic weightlifting, there is a much lower barrier to entry to clean or snatch a KB than a bar, making the benefits of these movements more easily attainable.
As I mentioned before, some things are not ideal with the kettlebell. My own example was getting my deadlift and front squat back where I want them. I won't be able to do these things with kettlebells because they just don't get heavy enough. And even if I got the biggest KBs available to work my deadlift, they would likely gather dust the rest of the year. But a selection of KBs from 24 to 48k, with some being doubles (probably 24, 28, and 32k) gives me so many options with very little footprint as compared to a bar, bumper plates and a squat cage.
One drawback to the KB worth mentioning are the weight jumps. The smaller KBs go up every 2k, but most KBs go up in size by 4k. Almost 9 pounds is a big increase depending on how close you are to your max. So the ability to load a bar more incrementally is an advantage the barbell has over the KB for some things - mainly when you're near your max. But then we're back to the increased footprint.
In short, every tool has its job. And not every tool can do every job. I just prefer using a tool that can do multiple jobs.