> The photosphere is no more well defined unless you specify a particular wavelength, or you admit defeat and accept averages as perfectly fine physical properties.

That stellar spectra (ignoring absorption lines) are broadly consistent with blackbody emission suggests that the size of the photosphere changes slowly with wavelength (i.e., that the opacity isn't a strong function of wavelength, otherwise there'd be a strong temperature gradient in the optically emitting regions). So from the standpoint of optical emission it's within the precision of measurements to think about it as as a single radius/surface. Or to put it another way, the change in photosphere size across the UV/optical/NIR is, for most stars, a small fraction of the radius. Thus the relative change in the size is small compared to the overall size. So while you're technically correct, "accepting defeat" won't be of significant practical importance to our understanding of the basic properties of stars (at least when discussing the continuum; absorption lines may have larger "sized" photospheres due to their increased optical depth at larger distances). Thus while talking about a single photosphere is not technically correct statement, it's nonetheless a useful way to describe the physical system.

I am certainly not prepared to ignore lines in this pointless internet debate! I did my master thesis on lines, how dare you?!

Furthermore, this is a discussion of the sun and not some far away "star" nobody ever even resolved to a disk.

On the sun we see the convection zones plainly, and thus speaking of a single temperature of what is clearly a feature with structure could be wery misleading (in certain specialised circumstances).