I have tried that type of extreme toe-in in my system before, but I can't say that I remember any particular sensation of the speakers disappearing more by doing that. The difference it made was that the phantom center would not totally collapse for listeners sitting off-center on the sofa, but the downside was a less defined/focused phantom center for a single listener in the absolute sweet spot. If I had to choose, I would never go for that type of "diffused disappearance" in favor of the more focused-sounding phantom center.
Ime a fair amount of radiation pattern control is required before time/intensity trading works well. I have never had it work well with conventional cone-n-dome speakers, nor with any speakers that have a wide-dispersion tweeter. I have had it work well with speakers that use a good waveguide, as well as with speakers that use a small, well-behaved wideband driver for the top end.
Eyeballing
@Thomas_A's avatar, it looks to me like his speakers use a small-diameter wideband driver for the top end, along with felt that is thick enough to actually be effective, and then his front baffle has nice large bevels along with a non-rectangular face which further reduces the already minimal edge diffraction effects. The increased directivity of the wideband drivers would further reduce the illumination of the cabinet edges. The tilt-back of his front baffle improves the time-domain blending of the two drivers, and reduces internal standing waves. Imo his is a very thorough design.
And more to the point of this thread, the above mentioned characteristics all reduce undesirable cabinet edge diffraction effects, which tend to degrade the spatial quality and can keep speakers from "disappearing". Potential resonances would also be minimized.
I don't think "downgrading" the overall sound and the fidelity should be needed in the hunt of having the loudspeakers "disappear", which I think both using an extreme toe-in setup would do to a single listener in the sweet spot (which truly is the only position where stereo works), as well as having an extremely high ratio of reflections in the listening room overshadowing the recorded information.
Ime with speakers which work well with time/intensity trading there is no degradation of sound quality when they are set up that way. Ime the primary tradeoff is a reduction in the apparent source width (soundstage width) relative to a more conventional setup geometry due to the significant reduction in strength of the early same-side-wall reflections.
With 45 degrees of toe-in and an equilateral triangle (speaker axes crossing in front of the listener), the central sweet spot is 15 degrees off-axis of each loudspeaker. With the same equilateral triangle and the speakers toed-in by a modest 15 degrees (speaker axes crossing behind the listener), the listener is at the same 15 degrees off-axis. So the change in direct-to-reverberant sound ratio from using a time/intensity trading setup geometry may not be as much as one would expect.
What DOES change significantly is, the time delay between the direct sound and the first strong lateral reflections, which now arrive from the OPPOSITE side wall. Imo this can have spatial quality benefits, which I can describe if you're interested.
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Since there seems to be controversy over the use of the term "disappearing" in this context, here is my usage of the term:
If you close your eyes and can easily hear the loudspeaker locations (using source material which is not hard-panned to one speaker of the other), then imo the speakers do not "disappear". If you close your eyes and the locations of the loudspeakers are not apparent, then imo the speakers do "disappear".