If you are distinguishing SUVs from crossovers, I'm not sure what you consider SUVs to be. The SUVs that are popular are crossovers. Thirty years ago, SUVs were body on frame trucks based on pickups, but that is a very outdated concept that has gone by the wayside.
In the US, some of the most popular SUVs, which I would also call crossovers are the Nissan Rogue and the Rogue Sport. The latter is sold in other countries as the Qashqai, I believe. Most SUVs today are unibody vehicles with AWD that is not intended for serious offroading nor does it have a low range. They are typically based on FWD platforms. So they are what I would call (and I think most people call) crossovers.
If we are discussing Subarus, and you call the Impreza a crossover, then you are left without a distinction between the Impreza and the Crosstrek. The Crosstrek only has a few cosmetic differences and a higher suspension, but that is what would make it a crossover to most people.
Body on frame SUVs with a selectable low range transfer case are a very small portion of the market even in the US these days. So the criticisms applicable to such vehicles aren't relevant to mass market SUVs in my mind.
Ok. Then how about the Subaru Outback or Forester? I'm talking about vehichles styled like an SUV, but shrunk. And per this article my __general__ definition aligns.
Regardless, the point is, the price of gas drives - no pun intended - comsumer preference. Only on HN can pointless minutia / noise be used to bury a topic / thought / fact.
Whatever you want to call them, the vehicles that most people buy and are generally called SUVs or crossovers no longer have a large differential in gas mileage compared to cars, which is why people prefer them.
It wasn't that long ago that I used to read comments on the internet about Americans being foolish and backwards for preferring vehicles with a trunk, instead of hatchbacks and wagons like Europeans did. Now Americans have essentially switched to hatchbacks (at least for new vehicle purchases) and yet people come up with a lot of pettifogging arguments why this is foolish and inferior because the hatchbacks are called SUVs.
Crossovers are much larger than Europeans hatchbacks, which are more like the Golf, Focus, Mazda3, etc. Despite being larger, they are not much roomier, and drive significantly worse. So again, it really looks like a preference for size over all other concerns.
I don't think that to the extent "crossovers are much larger" is meaningful, that it is accurate. Crossovers and non-crossovers come in all sizes, but we can look at the most popular.
One of the most popular mid-size crossovers in the US is the Nissan Rogue. Compared to the VW Golf (which I assume is one of the most popular hatchbacks in the place you consider normative), the Nissan is: 1.6 inches wider, 16.9 inches longer, and has 16.3 cu ft more cargo space.
The Rogue Sport is the smaller cousin of the Rogue, and compared to a Golf, is 1.5 inches wider, 4.8 inches longer, and has 7.4 cu ft more cargo space with seats down.
There is also a Golf wagon, which I think is in between the Rogue and the Rogue Sport in length.
The only substantive characteristic that defines a crossover these days that I know of is a few inches in ride height. Subaru has gone so far as to sell a crossover that is virtually a twin to a hatchback, with nothing more than a suspension lift (CrossTrek vs Impreza).
