Might be a favorite, but it's not very acceptable as a example.
Using a photo that contains obviously crushed down Black levels along with the "blown out light" caused by glare from sunlight isn't showing white, it's showing the difference between "glare" and the darkest area of the image where this is no back-lit Sun light. Such an example plays to a situation long pointed out as being a real issue when showing Contrast examples with a camera. The Camera makes the Blacks look blacker than they really are, thereby artificially increasing the appearance of the brilliance of the "Whites". Only if you had introduced an appreciable amount of Ambient light would you have leveled the Playing field between the darker and lighter parts of the image you offered up.
Show a true White, next to a Black for an example even closely worth considering, or in the least something like wbassett's "Top Gun" example.....something that still can show all by itself how a N8.0 Gray is muting those Dress Whites. And everything else for that matter.
That Screenie shows no snap at all. It's flat & dull. I've seem wbassett post far better fare. You too for that matter.
As stated a few times already, you cannot judge the individual performance of a Gray Screen showing Whites, against a White Screen showing Whites because the White Screen's whites will always look...and be whiter.
And you cannot (...or at least should not....) use blown out white Sunlight as an example.
However you can use a White against a Gray to show how much better the latter is at performing acceptably under ambient light conditions, and if that specific Gray has gain, how it will widen the contrast gap that has been shown that exists between a White and a N8.0 Gray which comes in under 1.0 gain, as is shown above.
All this stuff about "White vs Gray' and what Gray is better than another...etc, has it's roots first in trying to achieve better black levels but NOT at the gross expense of Whites and Colors. A True White vs Gray comparison will show that quite handily...and it's my obvious guess that is why you do not see those who have N-something Gray Screens that do not have +gain ever use a White that shows such a comparison . Such Screens comparisons will tell you whats needed to be told....it's just not what some people want to hear/see.
But whether it's a example meant for showing Contrast augmentation or Ambient Light performance, images don't lie. It's not so strange or hard to fathom that when someone does show something out of the ordinary, and that flies in the face of accepted norms, that some will discount or dispute the shown results. But if the shown example between to identical shade is well done and fairly balanced.....or well done with distinctly different shaded screens, if showing a 'difference' between the performance of the two or more examples is the goal, it can be done quite effectively and with complete validity as to the shown results.
As to "having" to depend upon excessive Lumen output to mitigate the loss of image vibrancy and decent looking Whites.....until recently that might have been all too true. For some with no lighting or wall reflection issues to deal with....nowadays if the PJ has at least a native contrast of 1000-2500:1, it is going to produce a great image on a 1.0 gain white Screen.
However on a Gray (...or white...) Screen that is under 1.0 gain, all that can be said is that keeping a PJ on High Lamp mode can help mitigate the all to obvious losses to a point that for many it will not seem to be much of a loss to them at all.
.....until they see that "one on one" comparison.