> If someone wants to understand the basics of antialiasing, or reducing image resolution with bilinear interpolation, the conceptualization of square pixels works perfectly
As Smith explains in the paper and I explained in the comment above, it's easy to get extremely conspicuous artifacts if you design a downsampling algorithm with the little-squares model, although if you're increasing image resolution you can frequently get away with it.
If you don't understand the formalization of the imaging problem that Smith is laying out—and it's clear that you don't—you aren't in a position to opine on how useful that formalization is. Applying that formalization will show you whether it's useful or not, and you can't try that until you understand it. My opinion from my experience is that I wasted a lot of time on the kind of seat-of-the-pants approach you're advocating, and now that I understand the rudiments of sampling theory, many problems that were intractable before have become easy. Learn from my mistakes instead of urging other people to repeat them.
> You call convolution with a square a special case, I'm calling it a reasonable first-order approximation for modern displays.
You are positing another opposition that simply doesn't exist. Perhaps you don't know what the phrase "a special case" means? A mathematical operation can simultaneously be a special case of a more general mathematical operation and useful for something, for example approximating a given display. And that is the case here. Being "a special case" of a more general case just means that everything that is true of the more general case is also true of the special case. It's not a way to deprecate the special case. It's a way to pointing you at a deeper understanding of it.
(Again, though, it's a zero-order approximation. First-order approximations are bilinear sampling and similar things. I think you have a lot of work to do before you can be in full agreement with me on all the math involved.)
You call convolution with a square a special case, I'm calling it a reasonable first-order approximation for modern displays.
And using a zero-order hold on audio samples isn't something most people frequently need to conceptualize. In fact, it's responsible for many people's great misconception that sampling rates above ~40 kHz result in noticeably higher-fidelity audio, because they think the DAC's output will be smoother. It's clear to me that you know better, but most people don't.
I'm in full agreement with you on all the math involved. It's simply that going around saying "pixels are point samples not squares" seems like it's going to be more misleading than helpful to 99% of people.
If someone wants to understand the basics of antialiasing, or reducing image resolution with bilinear interpolation, the conceptualization of square pixels works perfectly. More advanced antialiasing techniques are ultimately just subtle adjustments to that in terms of measurable output differences, which is why I stand by calling square pixels a reasonable "first-order approximation".