There's no mystery here and the differences between on and off axis placement are simple.
1. Sound is reflected from a bunch of surfaces in the car. We hear those reflections MOSTLY as changes in frequency response to the direect sound. They also contribute significant crosstalk (left ear hears right information and right ear hears left information). That crosstalk reduces the system's ability to sound "larger than the car".
2. The difference between on and off-axis sound from your speakers is very simply defined by the diameter of the cone. Frequencies that have wavelengths that are long compared to the diameter of the cone are radiated everywhere--to the front, the side and the back. Frequencies that are short relative to the diameter are radiated frontward.
2b. the high frequency response of almost all speakers has a peak. This is caused by cone distortion-a small part of the cone moves differently than the rest of the cone. That peak is "played" by a smaller part of the diaphragm, so it has a different dispersion than the rest of the cone. If you look at the off axis response of such a speaker, you'll see that the peak is not attenuated at the same rate as the rest of the high frequency response. This can be a HUGE problem and it's one of the criteria for choosing a crossover point.
3. If you mount a speaker on axis, the high frequencies will arrive at your ears direcetly and the lower frequencies will too, but they will ALSO arrive at your ears after being reflected off ADJACENT boundaries. The high frequencies will also be reflected by boundaries near your ears (side glass) but NOT from adjacent boundaries (because they are radiated FORWARD).
4. Reflections are attenuated because of the increase in pathlength (6dB for every doubling of distance). They are also modified by the material. Carpet doesn't reflect super high frequencies but glass does, for example.
5. So...a tweeter mounted off axis will direct more high frequencies into the reflecting surfaces and less into the direct sound. The same thing happens with a midrange (or a wide-bander).
6. When you equalize, you can't equalize the reflection differently than the direct sound from the speaker. That doesn't matter if your head is completely stationary because for every point in space, we hear the sum of the direct and reflected sound. When we move our head, we hear a different combiination. It's helpful to have the direct and reflected sound as similar as possible to be effectively equalized. This isn't possible in a car, so no matter how we mount speakers we'll still be confronted with this problem.
6. The problem is the worst when the off-axis response has a big hole and the on-axis response has a peak. This is common with 6-1/2" conponent systems where the woofer doesn't quite reach the tweeter. Sometimes, crossover designers who are focused on the on-axis response and ignore the directivity (off axis response) build a high-Q crossover to boost the response at the crossover. This makes this problem worse and can make the car sound bad when you listen despite a good curve.
All of this is why I suggest mounting tweeters on axis, using a small mid between a 6 and a tweeter, and keeping speakers away from the junction of the dash, side window and windshield.
Widebanders should ALWAYS be mounted on-axis if no tweeter will be used.