In his textbook TSPE, James McCawley gives an interesting taxonomy of adverbs which distinguishes them by what they modify. Clausal adverbs can modify any of S, V' (i.e., VP), or V, and this difference in what they modify is one factor in determining their placement and interpretation. Time adverbs like "soon", according to McCawley, are fundamentally V' modifiers, but they can be "Raised" to be S modifiers.
In general, McCawley says, we expect modifiers to occur either immediately before the constituent they modify or immediately after. Then for a time adverb like "soon", we expect it will go immediately before the V' that it modifies, immediately after that V', or if it is raised to become an S modifier, it will come immediately before or immediately after the S that it modifies.
Since each auxiliary verb in English, according to McCawley, heads its own V', this leads us to expect at least 3 possible positions for "soon" in a simple clause with no auxiliaries. "Soon he leaves" / ??"He soon leaves" / "He leaves soon". When there are auxiliaries, such an adverb ought to also occur after any auxiliary verb.
Overall, McCawley's theory works only moderately well. There are many problems.
Now, for something completely different, I'll outline my own theory of adverb placement in English.
Adverbs, as well as other clause constituents, have characteristic embeddedness, and since English is a right branching language, less embedded constituents come before more embedded constituents. When two constituents have equal embeddedness, they can occur in either order.
The differing degrees of embeddedness are 0, 1, 2, 3, unspecified. Except for 0, these correspond to the 1, 2, 3, chomeur of Relational Grammar. The 0 degree of embeddedness is for vocative nominals, root clauses, and performative adverbs like "frankly". "Soon" is a 2, so it should follow any 1 (subject). I would need an arbitrary adjustment comparable to McCawley's "Raising" to account for sentence initial "soon".