Are all introductory phrases dangling participles if the subject is not directly after them?

Not sure if I'm phrasing this right, but I will try (I hope it's not a dumb question). If you're being strict with grammar, everything can be a dangling participle if there's no subject directly after the modifier? Then it's up to the reader to decide if this is an adverbial phrase?

Here's an example:

Statistically speaking/speaking statistically, you have a greater chance of getting hit by a car than crashing in a plane.

The "statistically speaking" part could be interpreted as:

You are statistically speaking that you have a greater chance of getting hit by a car than crashing in a plane.

Even though, actually

I'm speaking statistically about the different chances you have of getting hit by a car compared to crashing in a plane.

if we remove the "you" or any sort of subject and put in a "there's a greater chance that..." instead, now we have a situation where things speak because of the omission.

???

I must be over-analyzing this... of course, one could say the subject is omitted, but one could say this for every dangling participle out there and say that it's just an ellipsis... -_-'

The answer to the question in the title is “no”.

No, not all introductory phrases are dangling participles when they are not immediately followed by the subject.

Having studied the subject for many years, some day John will write the definite treatise.

Properly modifying the subject “John”, surely the introductory phrase “Having studied the subject for many years” is not a dangling modifier. (See what I did here?)

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But when I see your example, it occurs to me that you may be asking a different question.

Generally, dangling modifiers are nominal phrases or adjective phrases that are meant to modify someone or something other than the subject of the sentence.

Adverbial phrases, on the other hand, don’t modify the subject, but the whole sentence. Even if the adverbial phrase is verb-based (such as “hopefully”), there is no grammatical need for the implied subject of that verb to be the subject of the sentence.

Hopefully the plane won’t crash.

is perfectly fine, and doesn’t necessarily anthropomorphise the plane: “hopefully” does not imply that the plane is hoping; it only implies that someone is hoping, most likely the speaker, possibly along with others.

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So what about present participles (“-ing forms” not used as a noun)?

Walking down Main Street, the trees were beautiful. Reaching the station, the sun came out.

Those are Wikipedia’s examples of dangling modifiers. Present participles-based phrases are usually parsed as adjective phrases, so they should modify the subject. When they don’t, as in Wikipedia’s examples, they are dangling modifiers.

Statistically speaking, planes crash once every million miles flown.

This is also a present participle-based phrase that doesn’t modify the subject “planes”. So if you parse it as an adjective phrase, it is a dangling modifier.

And yet, this example feels less wrong than the Wikipedia examples. As does yours starting with the same introductory phrase.

I guess the real question is: Can such a present participle be grammatically parsed as an adverb (similar to “hopefully”), even though it doesn’t end in “-ly”?

If the (pedantic) answer is “no, that’s not grammatical”, as it very well could be, then “statistically speaking” really is a dangling modifier when the subject of the main sentence isn’t the person making the statistical claim.