...I use apparent intersection for any intersection. Anyway, if I force the snap, I can then select one object and then select the object I'm looking to intersect with. I then know that I've gotten the object intersection. Well, that's how I've dealt with the issue you mention. At the same rate, I don't wish to appear to be telling you how you should draw with your software. I'm just putting out information. I'm enjoying this discussion, too. I think it will really open everybody's eyes to the pro's and con's of this particular funtion...
Yeah, using the apparent intersect rather than the intersect as a running osnap would work. Of course, then you need to click twice for an intersection, rather than once. Since I do a lot of drawing to intersections, and comparatively little drawing where POLAR comes in handy, I tend to find keeping intersect as a running osnap my default setting, rather than polar tracking+appint running osnap. For various tasks, I might switch. And so far, I've tended to think of appint as a kind of "intersect override", which I only use explicitely. It hadn't occurred to me to use it instead of intersect as a running osnap, although I can see how that would be useful in certain situations.
As is generally the case, one way may be better in some situations, the other better in others. It's best to know what options are available, and what strong points and drawbacks each has, so you can choose the most appropriate one for a given task.
In that vein, here's another factor to consider when deciding which is better for a given task: polar or ortho? With polar, you have to be relatively close to the intended direction to trigger the polar tracking vector; get too far off line, and the tracking vector disappears. With ortho, you can move the cursor through a whole quadrant without changing the direction of the ortho tracking vector. So, you can be "sloppier" with ortho. If all you need are 90° angles, this factor might make ortho easier/quicker to use.
