Is there an "inherent" problem with radical toe in,
The question is, what is ideal toe-in.
It depends, and lots has to do with how tweeters and mids sound off-axis. In many cases speakers are designed specifically for zero or no toe-in. This allows for a wide sweet spot and may actually smooth out the tweeter and mid response. Especially true for metal domes. Listening on axis is actually wrong for a lot of speakers designed for the average home listener.
The radical toe-in idea comes from the idea of attempting to minimize side wall reflections. The idea is to move more of the energy into the room before it gets reflected, hopefully improving imaging and spacial cues when other alternatives ( moving speakers away from side walls, absorbent panels, etc.) are not possible.
Take a look at figure 4 in this review for the MoFi coaxial speaker that's been in the news. The off-axis response is superb, but still you can see how the tweeter output goes down off-axis. Then also look at the on-axis response you can see how exaggerated the output is at the very top octave. This is a speaker you probably want to listen to somewhat off-axis for best response, but which will give you a very nice broad listening area.