Couple things:
- Actually, there’s a more accurate rule about subject verb agreement for native speakers. It’s not based on whether the subject is plural or singular, but by the presence of the “s” sound around the verb. If the word immediately preceding the verb contains an S sound, then native speakers will more likely choose a verb without an S sound, which is why subject-verb agreement tends to remain one of the most difficult grammar rules for native speakers to “correct.” Compare:
The groups of doctors is/are here.
The group of doctors is/are here.
In much the same way that the old “a before consonants and an before verbs” was categorically incorrect until the past 20 years or so yet still pushed in grammar books, aural rules like this one are slowly catching on, but subject-verb agreement still faces a lot of prejudice.
- It is not true inversion. True inversion is where the subject is actually in the object place:
Do they have hats?
There are hats in the window.
vs
There is a hat in the window.
The steak and potatoes example is good to identify which is the subject and which is the object:
When I order a steak, I get potatoes included? If yes, then “The steak comes with potatoes.”
If I order potatoes, is a steak included? No. “The potatoes come with steak” is clearly factually incorrect, but grammatically correct. Therefore, we know that the subject (your new promotion) is in the correct place and should be controlling the form of the verb. That the verb “comes” does not have direction allows the flipping of the subject and object to still make sense,
e.g. He kisses her, She kisses him, They kiss.
vs
He punches the bag, The bag punches him.
In the OP, it’s clear that the responsibilities comes after the promotion, you don’t do the new duties before the promotion.
- “Your new promotion” is not the object of the preposition “with”, which would be another condition for subject-verb inversion. Consider:
He comes with me.
vs
With me, he comes.
“Me” is clearly the object of the preposition “With,” even though “I come with him” is also correct.
True inversion means the object pushes the subject after the verb. If this happened with the above example, it wouldn’t work:
With I/me comes him/he.
It’s clearer to understand if we use “after” instead of “with”:
In the alphabet, B’s come after every A.
After A come B’s. (correct inversion, B is still the subject of the sentence and controls the s-v agreement.)
X After B’s comes A. (incorrect inversion, A is not the subject and “After” clearly cannot have “B’s” as the object.)
- The “with” is an example of prepositional fronting. In some cases, it is used to avoid having a sentence end with a preposition, e.g.
“That is the car which I came in.”
vs
“That is the car in which I came.”
However, the OP’s is an older form that is used to make sentences sound more pithy, elegant and/or formal that is rarely used in modern English today, but is usually taught just so modern users can understand older works or take grammar tests. I wouldn’t be surprised if the OP’s sentence was written before 1980, but the “With great power comes great responsibility” definitely was.
- Kind of a nitpick here, but “promotion” doesn’t decide whether it is comes or come, it’s the entire noun phrase, “Your new promotion.” Compare: “Your first of hopefully many new promotions…”
In summary: it must be “comes” because “your new promotion” is singular and it is the subject of the sentence.