This is probably just splitting hairs, but I don't think it is equally valid. Compared to the channel width, the center frequency is known / required to be set much more precisely. You could wiggle around by the bandwidth by 100s of Hertz and maybe lose some fidelity, or get some interference from neighboring channels, but you can't say the same for the center frequency.
It used to be relatively common for FM radio stations to run at over 100% modulation because it would allow them to be "louder" than the competition. Obviously this is illegal because it results in "spilling over" the assigned frequency band. But it absolutely was a thing.
Only by convention though. The radio systems I use have a configurable channel width and center frequency - there are only so many legal options. Center frequency is just a convention though - a 100kHz channel being defined as being bounded by (freq + 50kHz, freq - 50kHz) is no more logically valid than (freq, freq + 100kHz) or (freq, freq - 100kHz).
What I'm saying is that the filter that shapes the bandwidth (on either Rx or Tx) is not a brick-wall filter. The channel width isn't exactly as stated, because there's a gradual roll-off.
If I misspecified the bandwidth, I can still tune into and broadcast at the right frequency. It's not just a convention, it follows how the transmitted and received signals are actually processed. I do not think it's more logical because setting the center frequency and setting the bandwidth of the baseband signal are two independent operations. Conceptually, they are orthogonal concepts. So it's logical to specify them in an orthogonal basis. Choosing another basis, as you're saying, works. But the current "convention" is more than just a convention. It's the natural choice.
If I take my FM radio and take it somewhere that uses different channel spacing, I can still tune it to the advertised frequency. That would not be the case with what your proposing.
