This is a link to the Consumer Reports article mentioned above, "When Carry-on Luggage Isn't Carry-on Size." It's 4 years old now, so some of the brands and models tested may no longer be available, but the principles are the same.
If the sizer is constructed the same way as the picture in the article linked by the OP, a typical 22x14x9 bag should fit. But I've run into sizers that have an interior support structure which effectively makes them smaller.
My soft-sided 22x14x9 42L Eagle Creek bag like this is shallow enough to put it in one of those, but narrow enough to get caught under the upper support structure and make it very difficult to get it out.
It sounds like a real pain, but taking your bag, packed like you plan to pack it, to the airport and testing it for size and weight could avoid potential hassles later.
About a year ago, I got this 20.25x14x8 36L Eagle Creek International bag. The width and depth numbers are actually slightly smaller and are rounded up. It's obviously smaller and weighs less than the previously linked one. So far it's cleared all sizers and fit in every overhead bin, either turned on edge (the 8" size) or on its back, with the wheels at the back and handle at the front of the bin. I used it this past summer for a 5 week trip and the capacity was fine for how I pack.
I've had to gate check my 22x14x9 one on small planes and I was very pleased that the 20.25x14x8 one has not been questioned, so far.
As others have said, any gate agent could challenge it anytime. And if your bag is shaped a bit differently or looks too big, you can also be a target for gate checking when the plane is full and carry-on space is iffy.