No, the "alternative" approach looks strange in the 7 bit example.

1.0 lies on the right side of the bin 7. But 0.0 lies on the left of bin 0.

The standard approach assumes that we have centered samples: that zero is dead black, plus (and minus!) some uncertainty and so is bin 7.

If the sampling of the intensity is distortion-free (no clipping took place due to overexposure) then bin 7 represents a range of possible values centered around 1.0.

It is not a half-sized interval.

> This means that when converting floating-point values in the [0,1] range back to integers, the extreme bins have effectively half the width of other bins.

Under any interpretation whatsoever of the image samples, there is latitude for interpreting the maximum value 255 as being distortion: clipping from an arbitrarily higher value. Shifting things by 0.5 doesn't fix this issue of not knowing whether 255 means that an intensity close to 1.0 is being represented (no distortion), or an outlier intensity of 37.49 (severely clamped). That could go the other way too.

In other words, there is a possible bias in the extreme bin. The signal could be limited such that the bin's full sampling range is not in effect, or the signal could be overwhelming, so that values far outside of the range are clipped and included.

The only way around this is to make the highest value a canary which represents "clipped value". That is to say, 255 means "clipped datum", so that only 254 and below is sampling of unclipped signal. Machine-generated image (e.g. 3D rendering) then avoid the 255 value, and camera sensors are calibrated so that it doesn't occur when technical images are being shot.