A wagon or sportback I can understand. And thats essentially what a small CUV is based on, along with a bit more ride height and often awd drivetrain.
The CUV is popular because it's a really functional and practical design. You don't have to spend a lot on one, but you can. Maybe test drive some more and it'll click why so many people drive them. They don't all handle poorly either, some are downright fun.
The "CUV", compact SUV, is popular because it's higher off the ground. Because as other cars have gotten larger, people feel less safe with traditional sedans. Sedans, which worked well before because really people don't carry a lot with their cars most of the time. They've taken the hatchback design, since with rollover it's difficult to make those high in cargo capacity, and blown it up and thrown AWD on it. Take makes the car more expensive, it's more metal and plastic.
Doing that spoils the handling because now you've taken a chassis where the wheels would be parallel and lifted it. Making it so the body rolls more, providing a stiffer chassis feel, compounded by the additional weight for now larger components like the rear hatch. And you get a worse riding vehicle. I mean if the scope of the vehicles you've driven is just SUVs, then yeah, they might seem very sporty. But most of that is just marketing. That's why manufacturers don't really make sports cars into SUVs, because there's a lot of compromises in doing that.
On the contrary, having driven plenty of cars with and without AWD, adding AWD is a massive boon to handling for me, even outside of "rough" conditions like mud/ice/snow/gravel.
Especially since most vehicles’ AWD systems (especially if you’re talking crossovers) are really just “2WD but we can briefly engage the other two wheels if you’re trying to get moving on a patch of ice”. (One axle is not being driven except when the other is slipping, and in many cases there are speed limits above which this won’t engage. Many of these systems rely on clutch packs that, if they were engaged continuously, would overheat.)
CUV is far lighter duty, and far better in handling, driving dynamics and efficiency. Especially in models tuned for enthusiast drivers.
As for the efficiency of a sedan, you'll be hard pressed to convince me that putting non-cabin over the majority of the frame is an efficient design. Heck even a prius is a hatchback, not a sedan.
They wouldn't be so popular if every other car on the road didn't tower over conventional sedans. Why would you want a car that rides worse, is heavier, and costs more to buy and live with? People don't want vehicles that feel sunken into the ground and increasingly that's how sedans are perceived. It's a runaway effect.