Radical toe in once more

IME setting up bi directional speakers can be problematic. That back wave can be a killer if you don't treat the wall behind in in some fashion. I used dispersive material.  The success of crossing the speakers axis in front of the listener depends a lot on how much it is needed to reduce the effects of side wall/first reflections. It usually helps most when the speakers had to be placed close to the side walls. If side walls are not a problem then there really is little benefit other than changing the reflection pattern off the walls behind the speakers. I had Quad 65's for some years and it seemed to take forever to find the balance that worked best, butr I ended up with them pointed to just outside of my ears (no crossing over) and the rear pointing towards the room corners (I was 6ft off the rear wall). But, FWIW, it takes a long time (usually) to find the perfect placement for them to work, but do no minimize the need for rear wall treatment, Hell, I even tried Boston Ferns! Good luck.

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.

Thanks to both of you!

My room is quite large, I dont have major problems with side wall reflections or back wave boom, and the off axis treble response is quite smooth. So my speakers sound very good with radical toe in but also good with conventional toe in. I am just in two minds, regarding the front wave.

Something rarely addressed is the effect of floor and, more importantly, ceiling reflections. Crossing the axis of your speakers in front of you might get a more diffused soundstage (for the better?) because of changing ceiling reflections. Whatever, it does make a difference if you listen closely.

I am just in two minds, regarding the front wave.

If you had never heard of radical toe-in you'd be happy?  Then pretend you don't know what it is and keep things conventional.