Line Source - to toe in or not?

The answer is related to the phase relationship between drivers. With no toe-in, the tweeter strip will be either close to or further away from the listening position than is the woofer/midrange driver (the most common driver arrangement in line-source loudspeakers).

Some designers compensate for the resulting time-arrival differential in the speakers' crossover; others don't, expecting the speakers to be firing directly at the listeners head.

Many line-source designs are also dipoles, which complicates the situation. The sound coming out of the rear of the speaker is also delayed, in relation to that from the front. Then there are sidewall, ceiling, and front & rear wall reflections, all arriving at the ears at different times.

All the above is why experimentation is the only answer. Move and adjust your loudspeakers until you get the sound that seems "right" to you. What is "right" is somewhat subjective, and can change over time. You have to please only yourself (and your partner, if any). 

@bdp24 Missed the most common and obvious answer for a lot of speakers:

Some drivers simply sound better off-axis. It’s not uncommon for a speaker designer to take a tweeter that is bright, or rings on-axis and tame it by designing the speaker to be listened to "off-axis" or rather, with little to no toe-in. In my mind, the Focal inverted dome’s are famous examples of this.

It is also quite possible that speaker designers realize that speakers look better flat to the wall and voice accordingly. Some combination of these two accounts for most of these situations.

Erik has a point, but it raises a couple of separate but related issues.

A driver which is bright on axis, though not as bright off axis, will still be putting out too much high frequency energy into the room. It is the total power response of a loudspeaker which dictates how balanced octave-to-octave it sounds. If the tweeter is basically "flat" (putting out close-to-the-same SPL at all frequencies over the bandwidth it is employed), the designer uses a resistor to bring it into balance with the other driver(s). If however the tweeter exhibits a, for instance, rising-with-frequency output, that alone will not cure the problem. In his excellent series of Tech Talk videos on YouTube, Danny Richie (GR Research) explains how he compensates for this type of tweeter failing in the speaker crossover.

And a driver which "rings" does so not only on axis, but off axis as well. Ringing is a time-domain issue, though a driver which rings commonly does so more at certain frequencies than others. That’s why Danny Richie considers the spectral decay (aka waterfall plot) the most telling measurement a designer has at his disposal. There is no cure for the time-domain performance characteristics of a driver; if you want better performance, you need a better (one that rings less) driver. Makers and users of metal dome tweeters---notorious for their propensity to ring---sometimes dope the metal with some kind of damping compound. That is a help, but not a cure.

Many dipole planar loudspeaker (one type of line source) lovers hold in very high regard the ribbon tweeter Magnepan uses in their 3.7i, 20.7i, and 30.7 models. It exhibits very little ringing. The Magnepan ribbon tweeter is extremely good at the reproduction of, amongst other things, the sound of cymbals. The old Magneplanar Tympani T-IVa (a pair of which I own) contains the same tweeter, one reason that 3-decades old design still sounds so good.

By the way, Magnepan in their instructions for some models covers the subject of panel toe-in. Certain Magnepan models are designed to be listened to with the physical position of the panels at a certain angle relative to the listening position. That angle is related to---as I stated in my original post above---the phase relationship between drivers.