Are there any rules regarding position of elided Verb Phrase--before or after the Subject-- in Verb Phrase ellipsis?

Question

1. Defendants fifteen and younger are particularly impaired, and waive their rights much more frequently than do adults.

https://www.newyorker.com/magazine/2012/01/02/no-remorse

The un-omitted version would be:-

2. Defendants........., waive their rights much more frequently than adults waive their rights.

Would the following ellipsed sentences be incorrect?

3. Defendants fifteen and younger are particularly impaired, and waive their rights much more frequently than adults do.

4. Kids like candy, and so do adults

The aforementioned sentence seems correct. Does the logic/rule that makes this sentence "seem" correct to me apply to the previous sentence?

I don't think that it has anything to do with not terminating a sentence with the "ellipsed verb" --do/does/did, for the following sentences terminate with "ellipsed verb" and "seem" correct.

4. Few kids live where he does.

5. It is incorrect to assume that I dislike something just because my parents do.

6. It's beneficial to learn grammar, and many do so.

Answer 1

This is a special kind of inversion found in comparative clauses; it can be obligatory, optional, or forbidden, depending on the content of the clause. In your specific case, both "than do adults" and "than adults do" would be acceptable, though the former sounds a bit better to me.

Huddleston & Pullum (2002) have a good explanation of this phenomenon, and I don't think I can explain it better than they do. Here's a direct quote from p. 1107, slightly reformatted:

While a particular kind of structural reduction is the chief syntactic factor distinguishing comparative clauses from other clauses, there is also a difference with respect to the position of the subject, which can occur after the verb under conditions illustrated in:

i. Spain’s financial problems were less acute than were those of Portugal.
ii. ∗ The water seems significantly colder today than was it yesterday.
iii. It is no more expensive than would be the system you are proposing.
iv. ∗ It is no more expensive than would the system you are proposing be.
v. ∗ He works harder than works his father.

The effect of the inversion is almost invariably to place a contrastive subject in end position: in [i], for example, those of Portugal contrasts with Spain’s financial problems. In [ii], then, where the contrast is between the non-subjects today and yesterday the inversion is out of place: we need than it was yesterday. Note, moreover, that in [iii] the subject follows the sequence would be: it cannot invert with would alone, as we see from [iv]. The construction therefore has strong affinities with postposing (cf. Ch. 16, §4) – yet it also resembles subject–auxiliary inversion in that the verb normally has to be an auxiliary: we can have He works harder than his father works but not [v]. The construction therefore has something of the character of a blend between subject postposing and subject–auxiliary inversion, and this mix of properties is found only in comparative clauses.

(As is typical in linguistics literature, "*" is used to mark example sentences that are grammatically incorrect.)