When I was a console designer my job was to meet customers expectations. My personal opinion is that there is no such thing as a single perfect pan law, it depend somewhat on listening environment (headphones, near field, general home hifi, etc), and also the desired subjective result.
The accepted premise for utility while mixing for recording is that the pan law applies a first order correction for loudness as the source is panned across the sound field. The sole purpose of this is save time wasted in constantly correcting the fader level so the (level) mix doesn't change while panning. Of course this assumes you want the source to be the same loudness when centered, as when panned hard left or right. For advertising or program material that may end up played back after being summed to mono, compatibility of mono mix to steero mix is a consideration.
I wouldn't lose too much sleep over this.
If you really want to make this interesting, in a digital console, panning localization could be enhanced or manipulated by adding delay to selectively alter arrival time as a localization cue. (Note: relative loudness is mainly used as a back-up for determining localization, when arrival time is ambiguous.) If we use delay also, then the loudness law becomes more complex.