Would this then not bring up an important distinction between appropriate and inappropriate assumptions?
Because here, the clearly inappropriate assumption is that you have a flat field uniformly dense in enemies, such that a linear increase in radius corresponds to a quadratic increase in targets hit. That, I think we can all agree, is a ridiculous thing to assume.
However, it is not ridiculous to assume that if a weapon does 2d6+5 damage when you hit with it, then we can approximate that as 12 damage (2x3.5+5). Because there, we are generalizing across time, not space, and we are recognizing a real and pertinent truth, regression to the mean. We know the distribution produced by rolling 2d6, and we know that on average high rolls and low rolls will loosely match. We would of course need to account for critical hits, since those are a significant portion of damage (doubly so for specific characters, e.g. Champion Fighters), but that's just a matter of proper arithmetic, the fundamental idea that 2d6 "equals" 7 damage on average is not changing.
Likewise, when we consider an AoE spell, it is typical to assume that the spell is going to be used on at least 2, sometimes 3 targets, depending on the exact nature of the spell. Or, if an attack hits everyone nearby, you presume it's going to be used when there are 2 or more targets nearby able to be hit. Etc. These are most certainly simplifying assumptions, but they are not inappropriate ones. Quite the opposite--in many cases they are very conservative assumptions, erring on the side of caution, rather than excess, as your "triple the radius? Nine times as many targets!!" assumption would be.
Yet functionally 100% of the time, it is these assumptions which get attacked as "white room theory", as inappropriate ridiculous nonsense that cannot capture the true depth and complexity and meaning and virtue and beauty and holistic purity and (etc., etc., etc.) of "real" gameplay. Even though....it's literally just basic math and basic logic. If you only have one target, you aren't going to use an AoE spell on it, because AoE spells of a given spell level do less damage to each individual target, that's how they're designed. It would be profoundly illogical to do otherwise, unless you had (say) foolishly failed to pick even a single single-target spell to employ. Likewise, when considering long-run damage performance, it is literally just a matter of statistical fact that on average a greatsword is going to do about 7+mod damage per successful swing.
This is why I have such a hatred for the "white room" rebuttal. It's either actively foolish--disputing very basic assumptions as though they were somehow ridiculous nonsense, without giving the slightest reason for doing so other than "REALITY IS DIFFERENT! REALITY IS DIFFERENT! REALITY IS DIFFERENT!!!!!"--or it's willfully ignorant of basic mathematical facts.
You are completely correct that in the example you gave, the argument is foolish for "white room" reasons, namely that it has a broken and trivially false premise. But I have yet to see even a single instance of the phrase "white room" being used to reject a premise such as this in real life. It is--universally, in my experience--used to dismiss anyone who ever makes any argument, of any kind, that relies on statistical analysis.
IS. 
