Why "校车来了“， not "校车来着" and "校车正来"?
[Edited to discuss 正, 在, and 著]
There is a discussion of 在 and 著 in Li and Thompson's 1981 book Mandarin Chinese: A Functional Reference Grammar. They don't have much to say about 正. My own feeling is that this is usually used with either 在 and 著; it seldom, if ever, appears by itself. Sentences such as 他正吃飯 are simply odd. I am not a native speaker, so I'm ready to be corrected on this.

Both 在 and 著 are durative markers, but they still differ in meaning. L&amp;T's examples of the difference include:
他在穿皮鞋: He is putting on leather shoes
他穿著皮鞋: He is wearing leather shoes
Their explanation for the difference here is that 在 is used with persistent actions (actions that have some duration), while 著 is used with actions that result in a persistent state. 穿 can have either of these interpretations, so both sentences are good, but each has a different meaning. Again, I think 他正穿皮鞋 is just odd here, better to say 他正在穿皮鞋, or 他正穿著皮鞋. In neither case does this actually change the meaning, it simply emphasizes the durative nature of the action or result.

In the case of 來, I think the Chinese logic is that "come" is not a persistent action. Instead, it is what Quirk et al (1981) call a transitional action. Other examples they give are:
The train is arriving at the station
It looks like he is scoring a goal
According to Quirk, transitional actions do not have a durative meaning, and so for these cases English progressive has an anticipatory meaning, i.e. a period leading up to the transition. For these cases, Chinese doesn't use either 著 or 在 (since there is no persistent action or state). Instead it uses forms such as 快...了:
She is dying 她快死了.
She is coming 她快來了.

Since these are not durative sentences, many languages do not use progressive forms here. In this case it is English that is exceptional, rather than Chinese.