..., the -ing clause can see the entire apposed NP, but not the structure within.
Allow me to explain.
Sentence 2., as we know, is an example of a reduced relative clause, the relative pronoun (who) and its verb (is) having been omitted:
1. ...with Mr Smith who is a well-respected teacher.
2. ...with Mr Smith, a well-respected teacher. :tick:
The resulting modifying phrase 'a well-respected teacher' sees into the PP (with Mr Smith) and modifies the NP (Mr Smith), and not the P (with), because relative adjectival clauses, even reduced ones, modify nouns, and that, by the way, is the problem with our original sentence (3. below). The head of our phrase is a noun (lack), which is what the modifier sees:
3. The drawback of virtual school is lack of human contact (which is) providing students with daily ongoing interaction with teachers. :cross:
In (3.), the closest noun, from a non-linear view, is 'lack', not 'human contact'. That noun resides inside a larger phrase (lack of human contact), and so the modifier (providing students...) sees only the head noun (lack) and is not privy to the information housed within that phrase. In other words, it cannot see the noun 'human contact' and so cannot modify it. If it were to do so, then it would be able to modify either noun (lack & human contact), which would result in ambiguity, not to mention awkward readings. But we know that it doesn't result in ambiguity as evidenced by reversing the order here:
Lack of human contact, providing students with daily ongoing interaction with teachers, is a drawback to virtual school. :cross:
To fix the problem with, I suggest adding 'not':
4a.
Lack of human contact,
not providing students with daily ongoing interaction with teachers, is a drawback to virtual school. :tick:
4b. The drawback of virtual school is
lack of humancontact,
not providing students with daily ongoing interaction with teachers. :tick:
Note that, because of the copular structure, 'drawback' also plays a role:
5. The drawback is providing students with interaction. :cross:
<this is not the intended meaning>
6. The drawback is
not providing students with interaction. :tick:
<this is the intended meaning>
By the way, the meaning expressed by '(not) providing students with daily ongoing interactions with teachers' weighs heavier semantically than the meaning expressed by the noun 'human contact. That is, on its own the noun 'human contact' does not mean
providing students with daily ongoing interactions with teachers. It's the meaning housed within the larger phrase 'lack of human contact' that is being defined here:
7. The drawback of virtual school is lack of human contact, which means not providing students with daily ongoing interaction with teachers.
8. The drawback of virtual school is lack of human contact, meaning not providing students with daily ongoing interaction with teachers.